While you are directionally accurate, the flaw in your thinking is revealed by the fact that bad programmers also have high salaries, and plenty of five year olds have no problem being bad programmers, so there is clearly no need for above average intelligence or education to be a bad programmer.

As hard as it might be for this audience to comprehend, supply is limited simply because it is an undesirable profession. The majority of the population couldn't think of anything worse to spend their time doing. Much as the same reason why they don't want to go work on oil rigs and other such work that is high paying but what most people are unwilling to do.

High compensation is actually not as strong as a motivator as you might think. It can tip the scales if someone is already on the fence, but it doesn't suddenly make someone who absolutely can't stand something to change their mind.