Trust me, if I didn't need money, I wouldn't work. I'd do what I do when I'm on vacation or during the week-ends. I might do what's considered "work" by personal interest, but I'm not going to put any effort into something I don't feel like doing.
And who's going to do the real hard work ?
I mean, it's a fun idea in a way, and if automation does all the work, it might actually be feasible to a degree, but I don't see humans bursting their asses for nothing in the forseeable future.
Personally, I think money is probably the most significant invention in our history.
The big reason Gene Roddenberry's cashless society is so hard to fathom for a lot of people is, to me, partially the fact so few people actually get to do what they want in RL. The American dream is mostly the dream of getting by.
They're swamped with debt, bills, questions about how they're going to pay for medicine or education or their house. You have to run as fast as you can in the world to stay in place. It's hard to really wrap your head around having security if you've never had it.
I have a different perspective on this since I was, at one point, actually rich. I'm not now (thanks economy), but it's interesting note that my family members who grew up with security still worked. None of us were Paris Hilton rich but we all took jobs, essentially to make sure we just weren't living off the family. I did dishes until I finished paying for my college and later ran my own business.
I think the most utopian aspect of Roddenberry's vision isn't that everyone would be in the holodeck 24/7 (which might be the case for some) but that everyone can relax about where their next meal is coming from enough that they can enjoy themselves as well as reaching self-actualization. Study to be an engineer, scientist, or whatever.
Which actually makes sense of Picard's craziness to an extent.