I've met plenty of retirees who are rich enough to live off the earnings of a successful career, who find themselves re-entering the work force to out of boredom or to stay busy or out of passion for something. I don't think it's too far fetched at all that people who live on an idyllic earth in the 24th century work or start a "business" just for the sheer fulfillment of it. (do I think the 24th century will actually be that way? hell no, but if we accept star trek's premise that 24th century earth is a utopia, I totally buy it)
Now, would people become custodians for the heck of it? Doubtful, but that's what advanced technology is for. Chefs, singers, artists, architects, archaeologists, scientists, teachers, tour guides, tailors, carpenters, mechanics, engineers? I could definitely see people working in those careers (among others) just for the satisfaction if they already live on an ideal earth.
I buy into the idea that in the star trek universe, people on earth in the 24th century work to better themselves. That Earth in the 24th century is for the most part a self contained paradise where people don't have to work if they don't want to, but there are plenty of people who do for the satisfaction and self fulfillment. For all the jobs that people don't want to do, the dirty jobs, there are plenty of non sentient robots and other forms of non sentient AI.
Outside of Earth/core federation planets, it's a whole different story. Money is an important thing on the frontier.