It's not a problem, it's a feature.
In free market health care, those who can't afford care, die.
We as a society have agreed that's not acceptable and hence the regulations, EMTALA being one
Why not have a system closer to food stamps but for healthcare? i.e. the government will cover costs for the poor up to some amount.
We have exactly that. It's called Medicare + Medicaid. The govt fixes the price for what doctors/hospitals can charge on these plans and that's why doctors/hospitals absolutely hate Medicare + Medicaid.
For Native Indians, we also have the Indian Health Services.
For veterans, we have the VA.
That said, you nor I would really enjoy being on a Medicare + Medicaid system.
Having the govt. set rates, getting out of the way and leaving who and how that price gets paid provides the ultimate flexibility and value.
In many parts of the country, it is illegal to open up a new hospital without a government license. Existing hospitals often lobby to prevent competing hospitals from opening up.