> Some of the unions are non-traditional - for instance, the AMA (American Medical Association) effectively serves a role as a Doctors' union even though they don't advertise themselves as such. They control training into the profession, they are the sole arbiter of who can practice the profession, and they generally work to suppress supply below the level of demand (and therefore drive up wages).

None of this is true.

The AMA does not control training in the medical profession. That's determined by the number of residency positions available, which is capped by the AAMC, not the AMA. However, removing the cap wouldn't increase the number of positions, because those are funded by Medicare. The AMA does not control who can practice the profession either; only 25% of practicing physicians even belong to the AMA.

(The AMA is also not a union because it does not invoke a monopoly claim over the members of a bargaining unit, which is something that basically every union in the US does - and conversely, something which basically no unions outside the US claim - but that's all a separate matter).