The jobs that no one likes to do are done by machines. Haven't you read your science fiction?
I think that being taught that working is the right thing to do would be enough to keep most people doing it. Society has a lot of power over the individual. Also, it seems to be a recurring theme in star trek that these people are explorers--they're not producing much of anything, there just keeping themselves occupied. Notice that the only 'work' they do is fighting wars and avoiding disaster. I'd like to think that humans naturally try to avoid disaster, and I know for a fact that they naturally fight wars.
Other jobs seen in Star Trek include artists, traders, and therapists. Doctors, mechanics, holosuite programmers. Plenty to do.
And there's always something to buy--a vacation on Risa, strange alien art, and holoprogrames. And don't forget the joy of hoarding piles of gold-pressed latinum.
Ships still need dilithium for their warp cores. Replicators won't work without deuterium. And where does all that food come from, anyway? It's converted from nutritional supplements... surely not appetizing, but it's got to come from somewhere.
And though we've seen holograms and androids performing in many service positions, I can't believe the technology is available to everyone... and even if it is, who's maintaining it?
Also, the Federation in Star Trek does have currency. In the TOS episode, "The Trouble with Tribbles," the character Cyrano Jones sold tribbles for Federation credits. And in the DS9 episode, "Past Tense, Part One," we actually see a credit chip.
Source: Star Trek Encyclopedia
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