The patients.
That is who would be the doctor's customer...THE PATIENTS.
If all providers are reimbursed at the same rates for the same procedures and treatment, then the competitive free market shifts to the actual physicians. So doctors would have to compete for your care instead of insurance companies forcing you into a provider network. That would only improve patient outcomes because the doctor would need to be good at their job in order to attract customers (patients).
You also have the ability to "shop around" to find the best doctor for you. Right now, you don't have that freedom. You might think you have the best doctor, but what is your frame of reference? How do you know you like your doctor if you haven't had the chance to comparatively shop for one?
Isn't it more freedom to be able to go to any doctor you want? You can't under the current system (unless you want to pay for treatment outside your provider network), but you can under M4A.