I still cling to the idea that a moneyless society is only possible when you have almost unlimited energy and the ability to turn energy into matter, or at least rearrange matter, using replicators.
There is certain stuff that can't be replicated, like Dilithium, or Latinum, which is why these things still are worth a lot and even serve as a currency in some cultures outside the Federation.
It's also the idea that only Earth, human society, has no need for money. Humans are the most evolved and also naive culture in the Federation, after the Vulcans, who probably don't need any money either. We regularly see how humans are made fun of because of such things like having no currency at all. We also regularly see how Earth is spoken of as the Paradise. Which means Earth is pretty unique.
I guess humans adopted the no money thing from the Vulcans, shortly after WWIII. They also adopted some of their philosophy, which is why most humans now work to better themselves and the rest of mankind, instead of hunting for wealth, treasures and nationalism. Vulcan isn't considered the paradise, though, because it's a barren wasteland and Vulcans don't have emotions. Earth is the best of both worlds.