I can't really cite anything for my remarks, as they are based on vaguely remembered news articles over many years, but my impression is that the medical profession - in the US at least - has resolutely opposed any reform that would give the public access to information on the performance of individual doctors, hospitals, clinics or other elements of the healthcare system. The most prominent examples have had to do with histories of complaints and lawsuits.
The argument for this anti-transparency stance - and for disallowing patients to have their choice of surgeons - has been that they all have to learn by practice, and if patients were allowed to choose they would largely reject the junior staff, and the latter would never get any practice.
There is also a culture of solidarity amongst doctors, where an incompetent may get reassigned eventually, but won't be "outed" to the public.
And practice is supposed to be covered by med school and supervised residency, isn't it? The question mainly isn't about inexperienced surgeons, but about experienced surgeons who simply are poor at the actual surgical technique, and possibly won't ever get much better.
And choosing who gets which doctor based on, say, patient paying ability is actually better than the current semi-random choice - because it creates motivation for the worst surgeons to, well, try something else - if they're smart doctors, then they can be useful without cutting people up.
I look at it as a good thing since the alternative to letting quality seek compensation advantages is to accept a general malaise of mediocrity like we have in public education.
[1]http://www.telegraph.co.uk/health/healthnews/9935856/Heart-s...