The AMA works to prevent importing doctors from other countries, largely to maintain wages, but we don't have enough doctors.
Doctors boards and AGME (partly governed by AMA, but there is some amount of public representation) control residency admissions and board certification. We don't necessarily want low admissions standards, but there is a lot potential conflict of interest in constraining supply.
Some states, I think I read Florida recently, have started pushing back to allow in foreign doctors.