The health care payment system in the US is broken. Providers don't have any effective way of forcing payment; all they can do is transfer costs to those who will pay. This is effectively a very inefficient form of national health insurance, biased towards some of the most expensive methods.
We need a system where health care gets paid for, or doesn't happen. This means either some sort of government funding, or a system where if you show up without a means to pay, you get turned away even if that means you die.
First, make everyone eligible for no/low cost insurance, with no means testing. This should have a fairly low co-pay for doctor's visits, urgent care visits and most prescriptions, and a fairly high co-pay for an emergency room visit, with vigorous collection activity for ER co-pays.
The no/low cost version would be rationed. Money would be spent where it does the most good--that would mean that some treatments that are expensive compared to their results would not be available. You wouldn't be guaranteed a choice of doctors, and in almost all cases where there is a choice between convenience or low cost, low cost would win.
Traditional private insurance would be encouraged and subsidized at least to the cost of the basic system, and it would be required to have substantially equal coverage.
Another necessary part of this is an overhaul of malpractice. All doctors will make mistakes. All doctors will have patients with undesirable outcomes. The system needs to strike a balance between weeding out incompetent doctors and making every poor outcome a financial windfall for the victim or their family.