I don't know. After all Doctors are private people here too, earning their money per client. So they'd still make money in a nationalized system. A lot of hospitals in europe are private as well, so you can still earn money through providing health services.They'll cite ideological reasons forever on this issue but really just comes down to money. Some people are making a lot of money off of the capitalist health care system and they don't want to give it up. That's even if it means that millions of people suffer. It's just greed doing the talking really.
As for my doctor being picked by some bureaucrat. what makes you think this? I can pick my doctor freely (in fact switched to another doc last year), nationalized health care does not prevent this. Furthermore I'm still free to get 'more' healthcare if I wish: for a additional fee I can get private rooms in hospitals etc.