> And the schools prefer it (at least in the US) - limited highly paid doctors means they can charge exorbitant tuition.

What's the evidence for your position? Researchers who study this question have shown that the cost of medical education is significantly higher than the price assessed to students.

In other words, having more medical students would cost schools money.

I would've thought that the medical schools care about revenue, which is course can be increased both by raising tuition and by increase number of students.