doctor visa is a terrible idea, a) it would undermine the salaries of US doctors, b) it would drain doctors from poor countries where they are needed more than in the US.
IIRC, doctors already work on visas, and I don't think you would be 'pulling' doctors from other countries, not unless you're really good, which at that point you're only staying in your home country because you want to, not because you need to.
A) Lowering doctor salaries is part of the solution to health care costs. You could do this by educating them outside the U.S so they would have much lower student debt.
B) More people will enter the health care professions globally if there's a bigger market for their services.
