Well, there's a difference between "no currency" and "no money."I would imagine Star Fleet has some type of "SLEP" (Service Life Extension Program) for their Class One Starships since even in a society "without money", those assets must have some intrinsic value attached to them and it would be wasteful to just send them to the "orbital breakers" after a decade or two of service.
It's very clearly established in TOS that the Federation has "credits" and that people get "pay." This is beyond the obvious issues of trying to figure out how a society where there is no such thing as "value" applied to anything could possibly work, of course.
I think of this particular little bit of Trek lore as meaning "they have no hard, physical currency." Not that they don't have "money," only that their "money" exists as numbers in an account, not as bills and coins in their pockets. Basically, it's as if everyone has a credit/debit card and that's all they ever have to use.
I can't see any other way that things could work... NOR can I see any way that you can claim otherwise without saying "well, ignore TOS for the moment."
Fandom... definitely fandom. The only even "pseudo-official" bit on this is in Roddenberry's novelization for TMP, and in that one, he describes how the Enterprise is the first ship to get this treatment.Assuming that Enterprise was not the only Constitution Class starship to survive, it is conceivable that her update was in and of itself a SLEP-type upgrade, replacing older structures and updating systems and propulsion and was intended to be done on her sisters, as well (I can't remember if it was fandom or back-stage "history" that noted the Lexington was supposed to be upgraded first).
I prefer the fannish explanation (with the Belknap being the production version of the original testbed for the TMP-style technology) but none of it is "canon" at this point.