I ran multiple physician groups of over 400 physicians each and was an executive for private health insurance and government health care program contractors during my career.
There is zero correlation between the quality of health care and whether it is funded through for profit, not for profit or government health care programs.
Arguably, private health insurance has a huge advantage over government health care programs if for no other reason than they can refuse to contract with providers who produce bad outcomes or abuse the health care system. The government cannot.
I was always shocked by how much abuse goes on in the health care system. Private insurers have tools to address that, the government does not. There have been "bad actors" in the insurance industry and among providers. But bad actors in the insurance industry tend to go broke over time, while bad actors on the provider side don't.