Pretty much the same way I look at it too.To begin, a few quotes for reference:
"Don't tell me they don't use money in the 23rd century.
"Well, we don't."When the New World Economy took shape in the late 22nd century and money went the way of the dinosaur, Fort Knox was turned into museum."
Is there any way to reconcile the numerous and infamous references to there not being money in the Federation, or at least the core part of it, in the twenty third and twenty forth centuries?
Taking the twenty-forth century Earth as the example. Essentially a utopian society, possibly one that other Federation worlds aspire to, where no one appears to want for anything. Essentially limitless power is presumably provided by matter-antimatter technology. Replicators provide ample food, water, clothing and anything else people wish for.
The problem I have with the entire concept, possibly because I'm hamstrung by my twenty-first century mindset, is the overriding question "Why do people work in jobs if everything is handed to them for nothing?"
Without making too much social commentary on today's society, and also not to offend people who genuniely require benefits from the government, I personally feel that too many people today "sponge" off the state - avoiding work because they are handed money each week, faking injuries and illnesses because they prefer not to have jobs.
I personally have a job, but I only have one to get money. If the power to run my house cost me nothing, and a replicator in the house provided all my food, drink, clothing etc, I wouldn't have a job and be quite happy living a life of leisure. I'm sure the rest of you feel similar.
So my question is, will people really work in relatively mundane jobs, even in the twenty-forth century, when they don't need to? Yes, people would probably be Starfleet captains or senior staff for nothing because everyone can see the appeal, but what of other jobs? Public service jobs for example?
Do average people really go out to work to "better themselves"?
Or do machines take care of it all?
If so, is Earth effectively just a leisure resort where people are born, given everything they need for life and are free to pursue whatever existence they wish with no real responsibilities or requirement to 'give something back?'
Surely the often used 'credits' are not just a replacement for money, since if you're paid credits for doing a job and then use those credits to pay for your power and replicator bills, then this is money by any other name.
Apologies for the long post! What are people's opinions?
It's difficult to imagine a universe that doesn't operate on currency, but here's how I have always felt about it:
When the everyday things that you use and want can be provided to you at no cost by seemingly limitless technology, you get really bored and decide to do things just for the sake of doing them.
There was a time where horseback riding was an important skill for anyone to have, but now people who ride horses do so because they enjoy it.
While the Federation might not use a traditional currency system internally, there are many times when characters in Star Trek barter goods and services... and it would seem that the Federation does have some sort of monetary system for use with worlds outside the Federation.
At least, that's the closest I've gotten to understanding it.

But I also believe that what works in the Federation doesn't work anywhere else--including current-day society--and we're as mystified by it as the Ferengi probably are...