There's actually a lot of new med schools, both MD and DO, as well as a steady stream of foreign medical graduates every year. The problem is not the number of schools, at least in medicine, but the number of ACGME residency spots that remain artificially limited in the desirable (read: high paying) specialties. Tons of family medicine spots go unmatched every year but nobody wants to pay for 8+ years of post secondary education to make less than 6 figures.

There are also tons of law schools but most graduates take jobs that don't require JDs. It's actually kind of a joke now, even if you make T14 it's not a guarantee of landing a big firm partner track gig. It's not the education that's being limited since they're more than happy to take your money in exchange for a paper diploma; it's the actual desirable job placements. Which is the same in almost every field (academics stuck in post docs or non tenure track adjunct faculty, finance guys not making it to managing director, etc.)