The demand for medical care is essentially infinite, and the US is an example of what happens if supply is linked to demand via (distorted) "markets" in a country with great income inequality.
If you want a better idea of what a market would look like in health care, look at veterinary medicine in the US - it's regulated, with regard to drugs etc, licensed and all that other stuff, completely under government control, but:
the customer is normally reasonably well informed and can walk away from the deal (demand can drop, if prices rise)
and insurance companies have little role - no large bureaucracy of service denial has created an arms race of rakeoffs.
So prices are very low, compared with the identical services as supplied by a hospital to a human. And poor people take their sick dogs out back and shoot them. Is that what you are shooting for, in US health care ?
I would argue that your arguement, "The demand for medical care is essentially infinite" is false. There is no evidence of this. If it were true we would see infinate demand for medical services by those already covered by government insurance programs for the poor and for the military. In these instances, the poor and the military, healthcare is completely free in the United States. And we have never seen infinate demand for healthcare in either of these groups. The government picks up 100 percent of the cost of medical care for these people. Most people have better things to do than to seek healthcare services for non existent medical conditions.
There is a finite demand for healthcare services and products, were it not the case insurance companies could never quantify the risk. And not being able to quantify the risk, they could never issue an insurance policy.
The veterinary medicine business is less regulated in the United States, and yes, it is less expensive as a result. But no one is advocating shooting people in the backyard because of an illness. As I said under the plan I proposed, every one has healthcare insurance, and everyone has access to all the healthcare services and products they need.
What is different is that everyone is covered, and everyone pays for it. And costs are kept in check with the free markets (demand and supply). Demand will be grow as the population increases, but supply of goods and services will grow at a higher rate eventually leading to a price equlibrium.
Better and more innovative providers will be rewarded with being able to charge a premium for their services and from their innovations.