Sure there are (parts of) jobs that people enjoy doing. But how many people enjoy doing asbestos renovations, cleaning sewage pipes or repetetively operating a machine that might smash off their hand if they aren't cautious for a second?

to do it at random or some other voluntary arrangement, or perhaps the task can be routed around

That only works if the task doesn't require training, experience, skill etc. You absolutely don't want a newby to grab some diving equipment and inspect the inside of a full sewage tank.

I think the concept of having jobs with compensation isn't inheritely bad. The issue is rather that capitalism went completely out of bounds and that compensation has nothing to do with how pleasant or unpleasant it is to do a job.

In my mind, a theoretical solution could be a auctioning system where all jobs that need to be done start with the same basic compensation. A manager, a hairdresser or a construction worker would all make the same if they agree to do the job in that phase. Then everyone can pick jobs from that list. If a job cannot attract any applicants, the compensation needs to be raised (or working hours reduced or similar) step by step until someone agrees. But also in that approach it's difficult to adequately consider qualification for a job completely without discrimination.

Who is cleaning chimney for fun?