The "brain drain" is exaggerated - not that many Canadian doctors go to the states. The disparity in number of doctors per population existed before Canada had socialized medicine, IIRC, primarily as a function of the fact that the US has a lot more medical universities. And, according to recent studies, more doctors moved TO Canada than move FROM Canada.

Both the US and Canada have relatively few doctors when compared to the socialized medicine states in Western Europe. Italy has somthing like twice as many per captia than the US, or nearly that.

And we'll be in the same place as Canada with having too few doctors.

That didn't happen in any other Western country that adopted nationalized health, so far as I know.