Depends on who's complaining about a bottleneck.
The AMA caters to a base that is not happy with the influx of IMGs and DOs. The AMA inflates their numbers by auto-enrolling every allopathic medical student. The AMA is equally unhappy that the government using large scale funding levers at the residency level to overwhelm their efforts to tighten supply. By using money and their exclusive access to legislate, the government creates such a Venturi effect that they suck up all the available MDs, and all the available graduates from two other pipelines: the DO programs and the IMGs.
In 2017, the dissatisfaction of the 85% of physicians who don't belong to the AMA is ultimately driven by too much work.
Source: am physician. Have worked primary care, seeing 40+ patients a day, now completing a specialist residency. My work as an underpaid primary care doc was enough to keep 3-5 people fully employed (reception, x-ray certified assistant (sometimes 2), office manager, owner) from 8 am to 10 pm 7 days a week, while sending overflow to others.
Every one of the 85% of physicians who aren't in the AMA declined to renew their membership at some point. Many align with other orgs: almost invariably their specialty's organization, which aligns with the AMA but they are more professionally beholden to (for CME, board certification, etc). Many try to offset the ill effects of the AMA by aligning with other orgs like PSR or MSF or their local public clinics.
But the AMA has a bunch of offices in DC, and has had people in those offices, paying mortgages in McLean or Chantilly, or Silver Spring, <insert DC suburb here> for a century. Those people are motivated to continue their mission of lobbying in support of the legal grip of allopathic medicine, long past their original call to arms (licensure laws to cleanse the field of snake oil salesmen).