I dunno, I want to live an interesting life, so I'd volunteer to try ALL the jobs. Mining dilithium, serving aboard a starship, fighting baddies on the outskirts of Federation territory, raising a family, becoming a holodeck program writer... A life of leisure means you get to try whatever you want, and can always fall back knowing you'll be fine. I think more people would want to do stuff, like me, than you think.

Kinda like how every single pilot program and study they've done with basic income has had the same end result, no reduction in work force. People want to feel useful, and they want to get ahead. Maslow's hierarchy of needs, when everything else is met, people just want to feel needed.