The Rats have a solution to this: just make a law FORCING them to accept whatever the government decides to give them.
That was the law in Massachusetts under Mike Dukakis for a year or so. They had to repeal it after hundreds of doctors left for less enslaving conditions elsewhere.
Unfortunately, there is nowhere else to flee when they try this on a nation-wide basis. Most older doctors will probably just retire. Younger ones may move into other careers.