Triage, whether by overworked nurses or by auction or by private death panel or by public death panel, is not necessarily a problem created by administrators. It can be created by having too few surgeons, in which case whatever caused that (in a time of peace, no less) is at fault. Last I heard it was the doctor's guild lobbying for a severe crimp on their training pipeline, in which case blame flows back to some combination of doctors and legislators.
I'm not even talking about triage. It's not a matter of who has the worst problem, it's about which patient the nurses deliver to the surgeon and anesthesiologist. Literally just who gets scheduled and when.
You heard wrong. While at one point the AMA lobbied Congress to restrict residency slots, they reversed position some years back. However Congress has still refused to increase Medicare funding for residency programs. This is essentially a form of care rationing imposed through supply shortages.
https://savegme.org/
There is no "doctor's guild". No one is required to join the AMA to practice medicine, nor are they involved in medical school accreditation.