Well, just like what Picard said in the Star Trek "First Contact", that we don't have money in 24th century. But, is it possible in real life in a very advanced civilization like we are today or beyond? Ok, maybe there is no money, but no currency system at all? Is it possible?
1. Without money, what is the stimulation for people to establish private companies? Work for free? Oh common, we are human not an android. Without money, there is no urge to become rich, so I suspect that there is no private company in 24th century (Star Trek world).
There is no desire to create private companies because Humanity moved past that particular way of thinking and decided to work for betterment of everyone (not just the select few).
2. There are two types of humans in this universe. The diligent and the lazy one. So... say you are a diligent human, work hard for the Federation, and I'm a lazy human who love only masturbate myself in a holodeck. So..., without currency system, how could the diligent keep diligent, while the lazy get whipped to work? What is the reward system in the 24th century? If I can take everything without to do anything why should I work? A social work? Not everybody will do it unfortunately.
The 2 types of Humans you describe are nothing more than a byproduct of the environment (learned behavior).
There is nothing 'hardwired' into Humans making us one or the other.
We become one, the other, or something in between because we grow up under specific environmental influences that expose us to different behaviors and ways of thinking which we adopt... coupled with the amount of information we are exposed to (if you as a new-born baby were taken from say USA and left with the Amazon head hunters - you would grow up into a 'perfect' image of an Amazon Head hunter, especially if that was everything you ever knew - you would speak their language, adopt their cultural values, and you'd have 0 knowledge of anything else).
Money is not the sole motivator for Humans to work on Earth in real-life - otherwise, we would never have hobbies, or volunteer to help others without monetary compensation or rewards of any kind.
There have been scientific studies performed that demonstrated how money is a good motivator for repetitive tasks... but actually causes a detrimental effect when it comes to tasks that require problem-solving and/or creativity.
This model might be applied on a global scale if Humanity was actually exposed to relevant general education along if we created the environment that is by itself challenging/engaging/interesting to humans in the first place and based on cooperation as opposed to competition.
Most people who are seen as 'couch potatoes' mainly are because its either:
The only way of life they know... or, because they lack the purchasing power (money) to do anything else.
Besides, a non-monetary system could work.
Jacque Fresco and the Venus Project for example simply use automation technology to its maximum wherever/whenever possible to eliminate the 'need' for Human labor.
We ALREADY have enough technology in circulation in reality to automate 75% of the global workforce tomorrow if we desired to do so (although, most of the jobs people work on are unproductive to society at large).
The notion of 'human labor' has been outdated for decades in the face of how much we advanced technologically.
In less than a decade, we can repair damage done to the entire planet and create radically more advanced technologies (which would really be about 60 to 100 years more advanced if it actually reflected our latest scientific knowledge in practical application).
Humanity has been creating abundance for well over 100 years now with science and technology.
The monetary system was fitting for a time frame when resources were REALLY scarce, but this is no longer the case.
Today, humanity lives in ARTIFICIALLY induced scarcity - and sad point is, most of the planet doesn't even know it.
3. And what about private property? Like house, food, shirt, or maybe private holodeck, private replicator, and maybe a private starship, etc? I found that Picard's brother has a farm in France and Sisko's father has a restaurant, is it given by the government or what? And what is the privilege for Sisko father to live in his restaurant? Why not me, not you, or other people? If it is given and free, everyone has the right to take it. So why should Picard's brother or Sisko's father?
Roddenberry heavily drew on his ideas for TNG from Jacque Fresco's idea of Resource Based Economy and The Venus Project and probably wanted to represent it properly on TV in Trek... however, writers being what they are probably said that many of those things would be deemed 'impossible' or heavy to relate to (given the underlying premise that Trek was a USA show, and numerous people in the said nation had a tendency to basically project various notions onto anything non-capitalist as 'bad'.
Given the way it would work in a RBE system, governments would not exist.
And no, it wouldn't be anarchy.
The underlying premise of RBE depends on the global population being exposed to relevant general education - for example, all subjects relating to man.
This kind of exposure to education/information would allow people to govern themselves, arrive at decisions using the scientific method (as opposed to 'making' them), would be far less prone to being manipulated/used by others and would be prompted to think in a critical capacity (question everything) and to be problem-solvers.
In such a scenario/setting... the aim is to first and foremost provide for ALL human needs in a sustainable way (clean air and water, quality/nutritious food, clothing, housing, electricity, heat, access to relevant general education and access to quality medical care - and in this day and age, add in various household technologies, tools, and access to transportation).
Mind you we already had the necessary means to do ALL that, and more (several times over no less) for 100 years.
4. And what about food? you get rationing or you can get everything as you like without limitation? Say, even with replicator, they need energy, and we know that energy is not free in 24th century. They still need resource. And the government must take it from another planet (there is no Dilithium Crystal in Earth. They must imported it from other planet, and even if it's free, it needs a lot of work to bring it back to Earth). So how could the government prevent the people to waste the energy without any responsibility? Remember there are billion of people in the planet Earth, and everyone need energy to life. And unfortunately, Earth is not the only planet that need energy to life.
How little do people know of real life technology (and then go to apply such notions onto a society that is supposed to live in post-scarcity).
First off... Humanity has been producing enough food to feed 10 billion every year for just over 30 years now - this is using agriculture which is fundamentally outdated and has become damaging to our environment (we destroyed about 30% of arable land of the planet already).
For 50 years now, we had the ability to grow food in fully automated vertical farms that require no human labor, using haydroponics, aquaponics and aeroponics... no need for soil, pesticides, chemicals or GMO for that matter.
We can grow anything regardless of external weather conditions, the plants could also grow up to 5x faster (look into 'omega gardens' and the means of forcing the crops to fight against gravity) and the said structures could be designed to not only be energy efficient but to also produce energy and water.
1 fully automated vertical farm, the size of 1 acre and 44 stories high, employing a closed system would be able to feed 613 000 people.
This easily reduces our footprint on Earth by orders of magnitude as food can be produced in ample supply locally. Oh and we are already producing synthetic (but nutritious) meat (so no more need for killing animals either).
We had the ability since the 1940's to extract water from the atmosphere.
If every Human on the planet was as wasteful with their water as the average American (which they are NOT), the globe would have to extract 0.03% of water from the atmosphere daily, all of which would regenerate every 8 days.
This doesn't take into account desalination technologies that existed for over 100 years now (and the last time I checked, 71% of this planet is covered in water).
WE had the ability to transition completely by 1929 (or 1931 at the latest) around the globe to geothermal for baseload power/heat production (and eliminate harmful CO2 emissions in the process, using wind as supplement.
Humanity perfected recycling technology in the late 19th century, giving us the ability to recycle heavy elements.
Disassembly of matter into base elements and reconstitution into something else, or conversion of it into alternative energy sources.
By that point in our history, Earth already had tonnes upon tonnes of landfills that were teeming with raw materials which could have been used for creation of synthetic materials with superior properties and can be produced in abundance (negating the requirement of extracting raw resources from the Earth itself).
Tesla also demonstrated a working wifi power transfer around the same time-frame.
Energy in Trek universe is abundant and can be produced in several ways, just like in real life - except that Trek 'should' be able to do it better.
We can also do things orders of magnitude better - if we created our technology using superior synthetic materials that can be produced in abundance (and eliminated planned obsolescence - all of which CAN be done, and HAS been done in the past - the only reason why products and tech break down relatively fast today and provide low levels of efficiency is because we use 'cost effective'/'cheap'/'outdated' materials and methods of production - intentionally done for the sake of profits which in turn creates cyclical consumption and large amounts of waste).
5. And what keep people to work? Is it a hobby? Common, how could people work hard for their hobby constantly for the rest of their life? what if his hobby is playing the holodeck game (just playing and he/she is not even bother to make a holo novel program)
So either it is rationing, there should be another currency system that being used by the United Federation of Planets. Maybe it is not money, but they have another means to trade. Energy perhaps?
There is no need for Humans to work 'hard' today given the amount of things that we can automate - the only reason they do work hard (on unproductive jobs no less) is because the socio-economic system creates such a setting.
However... the last time I checked... why the heck did I bother helping other people by cleaning their computers from dust, re-installing the OS, setting up programs, etc... disassembled desktops and laptops and then put them back together... wasting 6 to 8 hours in the process?
Oh wait... that's right... because I LIKED DOING IT.
See... what you perceive as 'hard' and unattractive to do... some people would JUMP at the chance to do it.
In a world where Humans are FREE to work if the CHOOSE to... THEY get to decide how they will do the work... when, etc. (this actually produces far better results).
Also... on the notion of 'trade' and 'barter'.
In a world where money doesn't exist and everything and ANYTHING can be automated (this is scientific reality btw TODAY), why would people resort to trading/barter or currency when the system would be based on:
No 'private ownership' ... just on-demand access to what you need (and want).
People seem to forget that 'money' (today) provides ACCESS to using something whenever and how you need or want it.
If a material good that one person has and another one would like to use it as well... they simply need to make a request with the automation center and it would produce it using superior synthetic materials that can be made in abundance (as opposed to using inefficient materials that often times cannot be synthesized like its intentionally done now).
Note: Human wants stem from society/culture an individual grew up in.
Today we live in a world that promotes rampant consumption and more importantly, non-sustainability.
If you want sustainability... you need to expose people to relevant general education.
Right now, most of those who have the ability to 'afford' education in the first place are exposed to 'industrialized education' which main purpose is to see how good you are at following orders and to get a job and 'be productive' (in a sense of finding a job so you can contribute to the socio-economic system that is on the verge of yet another collapse - only this time, there will not be any recovery because no one is 'irreplaceable' seeing how Humans do specialized tasks - and computers of today are BETTER than Humans are, by orders of magnitude at specialized tasks - for which, they don't need to pass a 'Turing test'- and technology is becoming cheaper at far faster rates than before - companies go for cost efficiency, and Humans cannot be justified as a viable workforce when a machine can do the work many times better, faster, more efficient, without requiring rest, sick days or health care).
Now... this (rather long) post is supposed to give you an idea what could be achieved in reality - now try to apply that to Trek where its SUPPOSED to be their reality (mixed and mashed with current day perceptions that just don't make any sense for a Trek setting).
Some of these things were extracted from this particular article which you might want to read through:
It goes into good portion of details with numbers on what can be achieved using technology/resources at our disposal.
Needless to say that Trek Humans should have access to vastly superior knowledge and technologies at large, and abundance of resources.
If you are trying to reconcile different ways of thinking and motivations using perceptions from the present socio-economic system that works in a opposite way... it won't work, because, one cannot solve problems by using same ways of thinking that created the said problems.