Lizzie you seem to been keen on the term work but refuse the notion of a "market" with supply and demand. using your plumber analogy, if my pipes burst I get a plumber, my requirement is that He/She should be competent at plumbing.
When it comes to music being competent is in many cases unlikely to get you paid work, you must be outstanding either because of your ability in comparison to "competent" players or having something unique about your performance which appeals to audiences.
Many, many, more people play music than are ever going to be paid to do so. According to your argument we should stop them playing to audiences as the have not been paid to do so.
The problem is in the title of the thread. For a majority of musicians music is not work i.e. they don't get paid to play. It is a pastime/interest, hobby, release, etc etc. They may not get money but there are many other rewards, pleasure, sharing with others, sense of achievement, etc.
john