Free market for medical insurance.
Most people are covered by work, retirement, VA, Tri-care, Medicare, etc. Other people buy private insurance or pay cash for service.
Other people are not covered and cannot pay their bill or co-pays.
Send those unpaid bills to Medicaid that will study those people and work out a plan for them to pay their medical bills, college loans, mortgages, car loans, credit cards, fines, garnishment, child support, etc.
Medicaid run by the states to fit the local conditions and partly funded by block grants from the Federal Government.