The essential problem in this system is that, given no incentive to actually do anything beyond liking to do it, we are going to have a bunch (as in most everyone) of people that do little more than play golf, go sailing, go hiking, play video games, watch tv, etc. These people are also going to want a bunch of stuff (even though they are not making it). How exactly is that supposed to function when nobody really wants to do anything productive (because it is work, and why work when I can just play)? Or even if we somehow "make" everybody do something, what I really want to do, for example, is be a professional golfer (even though I have a 14 handicap), so all I am going to do for my "job" is practice golf all day every day (and there will be a lot of people joining me). Also - in allocating work out for "undesirable" jobs - who does the allocating? What if I refuse to do them because I don't want to?
The percentage of the human population that would actually do productive work (in any useful quantity) if everything was free is probably quite minimal. Even if someone likes their job, if all they get from it is the sastisfaction of doing it (but no real compensation), then very few people are going to do much of anything.