Assuming that you're referring to the AMA here, their role is pretty unclear to me. They appear to have played a lobbying role to get Congress to freeze residency funding in 1997 to avoid having lots of doctors [1], but for several years now, the AMA has at least publicly claimed that they've been lobbying congress to increase funding for residency slots [2]. Maybe they're lying? But I for one don't actually know who is keeping residency funding low.
[1] https://qz.com/1676207/the-us-is-on-the-verge-of-a-devastati...
[2] https://www.ama-assn.org/press-center/press-releases/ama-bui...
Common sense says that junior doctors should have the same practice rights as physician assistants - but the AMA refuses to let that happen. They are a medical cartel.
A few states have allowed junior doctors to start practicing medicine in a limited capacity, because every other doctor so damn expensive. But the AMA does not support those states' decision.
Like, could minting more doctors drive down costs for hospitals (that need doctors for services)?
Entrenched institutions are the general problem with America. It's the police unions protecting bad policing, the restricting of doctor supply via the residency bottleneck, and local governments preventing new building for burgeoning populations.
They're all the same problem really. Beneficial to the incumbent group at the expense of those they service. It's kind of amazing.