To be even more clear, the federal government already regulates the price of healthcare with the "open marketplace". They fix the price and coverage.
Discussion
The system you have is unfixable and worse than you described it. It is made for profit and exploitation. You cannot fix that, so there is no solution with such a base, you have to change that. So i am not talking about a system with such a base (see my others comments on the thread too). Forget about USA and its monstrosity even though it is all you know. Take another country as an example. There are other ways out there and you have one of the worst or the worst.
Oh, but thanks for the extensive answer.
Yeah, the US has some good hospitals, but the insurance system is terrible. Both public and private insurance are totally bonkers over there.
Even if you pay cash, the prices are often weirdly inflated.