The first half of the video below makes an interesting point about the cost of health care in the US. If you only consider public costs, the US doesn't spend more. It's only when you add in private costs that the US jumps above other countries. Public costs are in yellow...
Now he makes the mistake of assuming it's a problem with free markets when free in free market means free of government regulation. Government regulation drives the cost up. For example, the US government colludes with pharmas to enforce regional pricing of drugs so that the same drug is way more expensive in the US than Canada or Mexico.
He blames it on the different layers of payment. Medicare/Medicaid pays the least, private insurance the most. But that to is by government regulation which forces doctors and hospital to take less, so they turn around and push the rest off on private insurance.
The one thing he omits is that in the US people have more money and opt to pay more for care.