The way to solve this problem is straightforward.
To start with, neither the government nor insurers should be permitted to pay for routine and ordinary medical screening or care. By eliminating both from the system, the price of medical care drops around 50%. Yes, their overhead is almost half the cost of medical care.
For moderate health care, such as short term hospitalizations and lesser surgeries, insurers should be allowed in for those who wish to buy insurance; and government gives block grants to the states, who will use it to prioritize medical care for those who cannot afford insurance.
For extreme, catastrophic, extended stay care, it should be a separate block grant to the states. In declared emergencies, additional monies for this can be provided to the states involved.
The purpose of turning it over to the states is intended to create a price list of medical procedures. At the top of the list are things like cleft palate surgery, which is inexpensive, generally works, and substantially improves the quality of life. At the bottom of the list are things like multiple organ transplant surgery for premature infants, that is egregiously expensive and almost never works. The states prioritize procedures based on a finite amount of money. No money, no procedure, starting from the bottom of the list.
Another item that has increased costs is that we are mingling health care ( surgeries, medication etc.) with social care ( nursing homes). Those items should be separate, because a lot of health care costs is nursing home and caregiver costs. Hospitals should treat and street. if the government is worried about the social issues, then that should come out of a different kitty.