Except we've seen time and again that the Federation does have a currency and that Starfleet officers do get some type of Salary. Sisko bought land on Bajor to build a house. Beverley Crusher used credits to buy stuff at Farpoint Station. Nog and Jake have a discussion in 'In the Cards' that would indicate that money is definitely a thing in the Federation.
Except that all your examples are for commerce
outside the Federation. Deneb V (Farpoint), Bajor, and Ferenginar are not Federation member worlds. Other civilizations still use currency and capitalism, so Starfleet personnel on the frontier would naturally need a monetary stipend for doing business with non-Federation cultures. That doesn't tell us anything about everyday civilian life
within the Federation. The very fact that Jake, a civilian, explicitly says in "In the Cards" that he doesn't have any money suggests that it's not typical for Federation civilians to have money (although it makes no sense that Sisko doesn't give Jake an allowance for doing business with the shops on the Promenade or the like).
Federation citizens can clearly get their basic needs met, but the fact that not everyone is living in a mansion like Picard means that there is still some type monetary class based system in the Federation.
That's jumping to a conclusion. Just because differences in living conditions are based on money in
our society doesn't mean that's the only possible basis for the difference in
any society. That's a failure of imagination. In a society like the Federation, it would probably be assigned by need or by interest. Without the incentive to compete for wealth or show it off, a lot of people might simply
choose to live more modestly, because they don't need anything more.
And Picard doesn't live in a "mansion." He lives in the main house of his family's vineyard. Presumably that needs to be a fair-sized building to accommodate the staff, the wine cellar, whatever else is needed.
