Fiat REQUIRES a system that honors the stated value of the currency. If you have relatively small settlements acting on their own, no matter how advanced or established they are, a fiat currency simply will not exist for them to trade with one another. A currency MUST have some kind of intrinsic value to it outside of simply accepting a value that it possesses. Bottle Caps worked in the Fallout setting because early on after the decline they were an item that could not be (easily) counterfeited and were relatively rare to have in large quantities. Its scarcity was what made it valuable and thus acceptable as currency. Gold didn't have very many useful functions but it was so wildly scarce that, on top of being desirable for its prettiness, it was valuable because of that scarcity. The reason fictional depictions of post apocalyptic societies possess fiat currencies is because they grow large enough to become SOCIETIES, not simply settlements. The NCR was a nation, and their paperback was backed by their gold. Before that they used gold coins. These only worked because the NCR was a nation, not simply a hodgepodge of towns, nor was it a settlement trying to do trade with another settlement. A "few decades" would not be enough time, depending on the scale of the event that led to social decline to begin with, for groups of survivors to grow into a sophisticated enough and networked enough society for a fiat currency to be remotely possible. It would take much longer than that.