That assumes that all 150 members (which one might argue are only major members, and that there are others like Bajor that have a more probationary/potential status) have equal resources, and I'm not sure that would be the case. Nor am I sure they'd all have massive facilities even if they had resource equality as a benefit of membership. Different regions are going to have different specialties, and it wouldn't make as much sense outside a wartime setting for all of them to producing the same amount unless it was a necessity.
But at the same time, all 150 species that became part of the Federation have been members for years already (we are not counting prospective members like the Bajorans - who never did join during the course of DS9 as a show).
Those species would probably have well developed technological capabilities (in terms of space flight) and would have to be self-sustaining by the time they joined the Federation (meaning that providing for their own population would have to be a non-issue and other things such as space exploration and the likes would be done via creation of superior synthetic materials which can be made in abundance while using the least amount of energy and resources at the same time - heck, WE can do this, but don't because of the confines of the socio-economic system we live in).
For that matter, I doubt that SF would confine construction of its ships and structures to the SOL system (even though realistically, you could put millions of shipyards and space stations in just 1 system and you'd still have enormous/vast amounts of space to spare to make trillions more).
No, replicators use transporter technology to alter the form of matter. They don't simply create matter out of energy. That was one of the reasons the TNG TM talked about the idea of huge fleet scaled replicators not being practical. They would need templates to provide the matter and the energy involved presumably wouldn't be a fair trade compared to just replicating a meal. They're also stated to be unable to create substances like gold or dilithium, because those substances have very complex templates. Same reason they can't create living beings, although the aliens in "Allegiance" had replication technology that bypassed this problem.
Except that on-screen evidence states in TNG and Voyager that replicators convert energy into matter.
It was also said that the replicators are an outgrowth of transporter technology... but that doesn't mean it will work EXACTLY the same.
For actual creation of matter, replicators use plasma that powers the ship and convert it into matter (probably manipulating the particles of the plasma on a sub-atomic level).
Transporters convert matter into energy on one location then transfer that energy to another location and convert it into matter.
Replicators are power suckers (and for good reason).
Never was it mentioned that replicators require raw matter to create objects... it was stated they need energy.
Picard also mentioned to Moriarty in one of the episodes in TNG how Humanity discovered that energy and matter are interchangeable.
I don't really care about whats written on memory Alpha because canonical evidence takes priority, and in this instance, it doesn't support the premise that replicators need matter to create matter.
Or which part of 'Replicators convert energy into matter' don't you understand?
We know the very same process occurs in Supernova's in real life (conversion of energy into matter).
The Federation (if anything) is basing their technology on how nature works (and we are beginning to do so as well), and they are supposed to be hundreds of years more advanced than us (even though in some areas they appear to be sorely lacking - but that basically comes down to writers being uninformed and dumbing things down).
I generally agree with your interpretation of how Replicators can convert pure energy into matter. In the VOY episode "The Void", Voyager got a tech upgrade for the energy efficiency of their replicators from an allied member. Now they can replicate stuff at a significantly less energy cost (The Federation tech folks must've been happy when they discovered that piece of tech back home once Voyager returned given the replicator economy). Note they mention that the replicator uses energy, not just matter converted from one form from another.
I'm sure the replicator can convert matter from one form to another, there are many guides in ST Tech Manuals that mention matter tanks for replicators, however should the need arise, they can convert energy into matter. I guess by the time of VOY, energy is so abundant, that carrying massive amounts of matter tanks isn't necessary when they can store / generate so much power.
If you look at things from a logical perspective with Replicator 'Energy to Matter' vs. 'Matter to Matter' conversion, it should probably be cheaper in total energy cost to convert an existing form of matter like Carbon, add in the appropriate amount of electrons / protons / neutrons / etc to turn 1 atom of Carbon into 1 atom of Iron then to start from scratch and have to form each Iron Atom out of pure energy.
So there is value to having matter tanks, but not necessarily for basic atoms, but for probably some of the harder to produce materials like Duranium which is probably a very complicated alloy of some sort from my understanding. You don't need alot of matter tanks, but just enough to make it cheaper on energy costs to make more complicated matter.
Basically there is a valid argument for both methods of replication based on efficiency. Since Energy / Matter is the two most important resources within the UFP, I would assume that they would do everything in their power to make replicators as energy efficient as possible and try to run more traditional forms of material fabrication if it made energy / resource sense to do so.