No. Instead, we should simply offer enough openings in medical school so that we have enough doctors to satisfy the demand for health care. There are plenty of American students who would make good doctors, who are turned away because of the limited number of openings. American students have an advantage, in my view, because they speak the language, and they understand the culture from the outset. We don't need to import medical students from abroad to satisfy our needs.
I don't have a problem with foreign students coming here, though, provided that they pay their own way, and don't reduce the number of available slots for American students. Personally, I think that a doctor makes enough that he doesn't need to have his education subsidized at all.
I agree with you a large part of why the medical system is broken is because the AMA and its subsidiaries limit the number of students who can attend medical school.
Then add in the lawyers, and it really drives up the cost of medicine.
I had a hairline fracture in my wrist 2 months ago, and it's cost me over $6,500. $3,200 for the ER and $3,300 for the Orthpaedist.
In the end I could have gotten a simple wrist brace from Walgreens for 20 bucks and saved all that money.