I've no doubt that the ultimate winners would be the procedure-based specialists but it's hard to imagine that an open market wouldn't reward those in under-resourced specialties in the short-term. Of course that's assuming that the private sector was willing to take any responsibility for emergency care as it is unlikely to be profitable any time soon.
Oddly, emergency physicians in the US are very well remunerated and, given its short training pathway (3 years post-medical school !), it is one of the most competitive specialties among new doctors. I agree that this isn't intuitive given that emergency patients are less likely to insured, etc.