Full transparency could have negative unintended consequences. For example, if surgeons knew their success rate were public, they would be incentivized to take easier cases. Who would take a difficult case if they knew it would constitute a bad mark on their record almost for sure?

Fundamentally, the issue is that it's impossible to observe for any given patient if that patient's outcome would have been better with a different surgeon. This is the same challenge we face with evaluating drugs: many more people who take aspirin survive than those who take anti-cancer drugs, but this likely reflects the kind of person who is taking each (people with headaches vs. people who have been diagnosed with cancer). To solve the problem there's no way around randomized trials. So, one idea would be to randomly assign patients to surgeons.

(Transparency might still be better on net, but important to keep these issues in mind.)