Stats are hard because of all the other factors involved. It would be quite likely for the very best surgeons to have lower survival rates than mediocre surgeons, simply because the mediocre surgeon would refer the objectively harder cases to the expert, which would give better chances for that particular patient while lowering his 'batting average'. And if you give direct financial motivation for doctors to avoid taking such patients, then it's a bad thing for the whole system.

Stats can help you weed out obvious outliers - i.e., the ones who should be kept away from patients; but it's not so simple to make them useful in actual prioritization.

Success rate alone may encourage doctors to form other kind of risk preference in general. The fundamental issue is huge information asymmetry with different conditions. I guess there is not a simple solution to this. However, different simple solutions from different levels may benefit both good doctors and patients. Doctors and their organizations has much bigger power than patients do. Information could be something powerful to make the situation better, but not even close to perfect.

It would be useful in part because another surgeon can assess how well he is doing before actually stacking up enough bad/good statistics to notice. It's also useful for training, just like watching yourself swing a golf club or a baseball bat or rereading your old code can help you, with the aid of others, see what you could improve on. Doing the wrong thing over and over in a vacuum doesn't make for much learning..