I think your first point may be valid. (I'll even add to it that good but mercenary doctors may leave for other countries where they can make much more money.)

However, the corrollary isn't. There are bad doctors in countries with socialised medicine. This doesn't mean all doctors are bad, and it doesn't mean all care is crap. And I say this with experience of medicine from the patient end in Britain and Canada. (I'll also say that I had a US friend with me once when my son had an accident and we went to Emergency in Britain and she was very impressed at how good and fast the treatment was... and how little admin there was.)

Also, I've heard in the US if you want a "top surgeon" you can get one if you can pay for it -- and that's wonderful, except if you can't pay for it. In Britain or Canada, you get a random surgeon, who might be the best in the country or who might be the worst, according to what's available and how sick you are. It's random chance and need, not whether or not you can pay for it, even if you are paying for it. So if you imagine the life of a British or Canadian "top surgeon" they'd be assigned to the hardest cases, and a US one, to the richest.

It seems so much more fair to me, but I suppose if you're looking at it from the POV of a rich person, that wouldn't seem fair.