What happens when a not-so-good doctor charges very cheap and start a price war? Or to make it affordable, the doctor cuts corners? Who's to tell the doctor to what to do?
Who watches the watchmen?
At least with this model, the patient is choosing the doctor, paying him, and receiving he care. So if he cuts corners in a way that makes the patient less satisfied (eg. very short appointments, cramped/dilapidated office, bad on-time performance, office in a bad part of town), the patient can choose to go elsewhere. If it's the one place the patient's insurance will cover thanks to the reduced price from cutting those corners, the patient has no real choice.
You end up where we are now where mediocrity is rewarded and excellence is punished, and they both cost the same.
It is well past time to allow some market forces to work in this area. At least things would be more rational.