The reality is that Canada, and other nations with government run health care, *are* able to retain doctors. Hypotheticals are one thing, but reality is quite another.
That said, there is a flow of practitioners across the border, north to south. I don't know about the other direction, and suspect that it's smaller. You can make more money in the USA than in Canada.
As for the state of health care in Canada, here's a another little dose of reality: MRI machines and the like are not free. The USA's astronomical health care costs are driven, in a large part, but unnecessary procedures and tests. The fact that there is an MRI machine down every hall sitting idle, does indeed cause a trend of more MRI tests. Canada doesn't have an MRI machine down every hall, that's a fact.
There's a benefit of being able to get an MRI on a moment's notice. That's real. That saves lives.
There's also a cost.
Much as I dislike the idea of placing a dollar value on human life, we have to recognize that our attitude of "no amount is too great" is a big slice of why we're going broke on medical care in this country.