This is always something that I have wondered about. It has been common across the games, being found on dead bodies and in old stores but it has always just been cluter for no reason. It makes sense to exist since caps are now the currency but is there any use for the pre war money in Fallout 76? It seems to be something I find all of the time.
The main use I have for the pre war money is for making cloth. I know it seems weird to use old paper to create a cloth but thats how it works. If you visit a crafting station you will be able to scrap the money and turn it into cloth. It is actually one of the best ways to obtain cloth since, as you said, money is quite common.