Even as a hypothetical that's an unrealistic question. Since we have a shortage of doctors in many regions and specialties due to price controls and educational pipeline bottlenecks, even if it was possible to rate doctors with a reasonable degree of accuracy (and in reality this generally isn't possible) some patients would still end up getting stuck with the worst performers. The only difference is that instead of the selection being mostly random as it is now, under your hypothetical the patients who would switch to the best doctors would be the wealthiest and best informed; the poor, elderly, and illiterate would continue to get screwed. Is that really the outcome you want?