How about a two-tier insurance system that incorporates Medicare and Medicaid? The problem private insurance companies have is that there is no limit on their risk, so premiums only rise as the pool of patients gets sicker. Keep private insurance policies, but limit their total coverage to some yearly amount, like $50,000. Then allow anyone to buy into Medicare or Medicaid from their paycheck. You now have two policies. When your private benefits cap out, Medicare/Medicaid take over for that calendar year.
We have to divide up risk over as many markets as possible. The idea of making insurance state-agnostic isn’t practical because health care costs are all local. There is no national cost for heart surgery. With a federal component, you do effectively have a national insurance policy for particularly bad events. Medicare/Medicaid would get more funding because every worker is buying in and a relative few will use benefits in any particular year. The risk profile for Medicare improves dramatically when tens of millions of young workers are paying in for that supplemental catastrophic coverage. Private insurance premiums can fall because the total risk for any one patient is greatly reduced.
Now, we have a worst of both worlds system — a private system that is getting more expensive and a government system that lowballs providers, leading them to make up that difference by passing costs on to the privately insured. We could turn it into a best of both worlds system by making Medicare and private insurance into a unified system.