What I hear you saying, is that surgery, especially serious kinds of surgery, is basically a crapshoot. If you go to a mediocre hospital, you might get the doctor that you want, but he will not be one of the leaders in his field. The quality of the ICU may not be on a par with a major institution. If you go to a major hospital, it might just not be the chief honcho who actually does part of the procedure.
So, bottom line, it is still, IMO, a matter of probabilities. As they say, "You pays yer money, and you takes yer choice"!
OR you just be sure to ask tons of questions. like how many of my procedure have you personally done? (also I ask if they have a dedicated CICU or if the nurses in the ICU take care of heart surgery. brain surgery ect, I PERSONALLY prefer where the nurses deal with just hearts 24/7)ARE you in the OR the entire time or at least close by. IMO For routine first time valve replacements, most of the local heart centers/university centers probably have plenty of experience to handle most things that can come up, and probably can do first time replacemnts in their sleep(especially as Al said IF they do heart transplants) Ask how many they have done and what their stats are like.
It's the complex cases/ MULTIPLE REDOS that need the best of the best people that are experienced with seeing the problems that come along with that and can deal with issues without having to stop and think, (and then ask questions dealing with your particular heart issues, like we knew before Justin's last 2 surgeries his heart was fused to his sternum with scar tissue, so we asked the different surgeons, WHAT their plans were to open him as safe as possible ect)
YES it can come down to a crap shoot but for first time valve replacements the odds are like 99% in your favor.