Residency programs are more restricted by funding for residency spots, not by the AAMC. Funding is, very weirdly, provided by Medicare. It's all a tangled mess with lots of weird stakeholders, but saying "doctors are using rent seeking behavior to limit new entrants to the field" is a bit disingenuous.
https://economix.blogs.nytimes.com/2013/12/17/how-medicare-s...