The other problem with a moneyless society, is how were people compensated when their cash, property, products, farm goods, and stock certificates suddenly became worthless.
Look at it this way. Imagine if energy was free and in abundance (antimatter). Now imagine if it could easily be converted into matter (this is how replicators work). This technology wasn't yet mainstream in mid 22 century, but it's safe to assume that this mysterious "new world economics" was based on this.
Free energy for everyone means also free food, free clothes, free water... And as for housing, industrial replicators take care of that. Homes are practically costless, so we can assume that in the UFP every citizen is entitled to one.
Here ya go. Utopia.
BTW, it's safe to assume that some form of currency still exists (hence the motivation), and it is mostly used for aquisition of "luxuries", like Scotty's famous boat, Admiral Paris' shuttle, or those antique glasses Bones bought Kirk for his birthday.