It's a little more-complicated in that one of the major bottlenecks comes not from the private organizations per se, but from Congress--though I wouldn't want to underestimate the effect of lobbying.
> In the Balanced Budget Act of 1997, Congress capped the number of residency positions that Medicare would fund at each teaching hospital at 1996 levels.
Yes, and the AMA, along with other associations, supported the cap, issuing a statement that claimed "compelling evidence that the United States is on the verge of a serious oversupply of physicians."
> In the Balanced Budget Act of 1997, Congress capped the number of residency positions that Medicare would fund at each teaching hospital at 1996 levels.
https://thehill.com/opinion/healthcare/5550556-residency-cap...