1) The incentive to innovate in the overall medical field is fulfilled by the existence of private hospitals, which according to my OC wouldn't be banned or cease to exist. They would coexist alongside the public ones.
2) Behind your statement lies the necessary asumption that the medical staff would not provide a good service to their patients because the government would pay them less than private hospitals. While it is a spectrum, most decent doctors won't treat their patients worse because they are getting paid less, something that is not the patient's fault nor responsibility.
Besides, one does not choose to get ill or suddenly feel in need of medical care.
Your use of the word "customer" to refer to a medical patient sickens me.