Earlier quoted context omitted.
Public+private spending on healthcare in the US is 2-3x that of public+private spending on healthcare in the rest of the OECD. See the chart at https://data.oecd.org/healthres/health-spending.htm ; we pay more in taxes than any other OECD nation does total for healthcare, and then pile individual spending on top of that .
The US government does a lot to increase health care costs. For one example, the government empowers the AMA to strictly limit the number of seats in medical schools, the purpose being to limit the supply of doctors to keep their fees high.
You asserted "Just because it's 'free' doesn't mean you aren't paying plenty for it", but the places where it's "free" are paying less. You're highlighting issues specific to the American system in an apparent attempt to argue against European-style systems, which is... odd.