The ship also cleans itself. The Federation is a post-scarcity society. They've figured out how to change matter into energy and back again. That does change a

The ship also cleans itself. The Federation is a post-scarcity society. They've figured out how to change matter into energy and back again. That does change a lot of things. We don't get to the Federation without solving scarcity. And while no one is being paid to be on that ship (although that is debatable as there does seem to be some form of currency that individual Starfleet members receive and use), there is competition to be on that ship. Being on that ship is the compensation for the work. Being one of the few selected to essentially be in this sort of elite class is the privilege. And even on the ship, there are differences between crew members. The captain's quarters are better than the lower officers. The captain has his own private office just off the bridge. And being a television show and work of fiction, they get to gloss over a ton of stuff. The acquisition and creation of the materials to build something like the Enterprise is as much a fantasy in the work as is the fact that they can replicate Earth-like gravity in the middle of space.