But the track record for such a doctor will clearly see that they aren't tackling the difficult cases. Would a doctor want a high success rate if it comes with a reputation for only taking easy cases?
Even if the answer to the above question is Yes, the reduced number of doctors willing to tackle difficult cases will be able to charge higher fees. So at some point you would reach a market equilibrium where the desire to tackle easy cases is balanced by the desire to earn a higher income. That is, when compared to the current system the easy cases will become cheaper and the more difficult cases will become more expensive - but maybe that is an acceptable outcome if it means the system as a whole is more efficient?
It depends on the goals of the doctor. If the doctor aspires to a massive volume of fixed-rate, "easy" procedures (look at cataract surgeons benefiting from the advances in that field while insurance and Medicare reimbursement rates remained constant [and high]). I'm not knocking those docs; they provided real and tangible benefits for millions of patients with cataracts and I don't begrudge them their money. It's just super amusing to me to walk down the multi-million dollar warbird parking area and have half the owners be eye doctors.
As for aspiring to have a reputation for efficacy in difficult cases and assuming that you'll be able to charge more due to market forces? I don't see that playing out in any Western medicine economy. IMO, you can't build a functional ecosystem around the very few patients who are self-paying and willing to pay large sums for better care.
Very wealthy individuals and pro sports teams are the only customers I can see for that. The overwhelming majority of people (far in excess of 99%) are going to have two hurdles to procure your expensive services. First, they have to find and select you. Second, they have to convince their insurance provider to pay your rate, instead of the "going rate". That seems uphill, probably steeply so.
As someone who had a serious illness last year and who is not in the top 1%, I can promise you I would have crawled over broken glass if I thought it would have improved my chance of survival. I certainly would have paid a large chunk of my net worth to switch to a doctor who had a significantly better track record.
I don't understand why the medical insurance market wouldn't work. If the insurance company won't let me switch to a doctor who has a better track record, won't that insurance company get a bad reputation and lose business? U.S. doctors have a better reputation than Mexican doctors and in this case most people pay for insurance which covers treatment by the more reputable doctor - I imagine the same effect would apply between doctors within the US if there were a objective track record which identifies the better-performing doctors.
Even if the answer to the above question is Yes, the reduced number of doctors willing to tackle difficult cases will be able to charge higher fees. So at some point you would reach a market equilibrium where the desire to tackle easy cases is balanced by the desire to earn a higher income. That is, when compared to the current system the easy cases will become cheaper and the more difficult cases will become more expensive - but maybe that is an acceptable outcome if it means the system as a whole is more efficient?