> for decades
You are retelling what happens in a very short period of time, ignoring dynamics.
Decades is nothing for a country. You could look at second-world countries which were pioneers in universal healthcare and universal pension funds. For most of them it didn't last long. Even though the "universality" was questionable. These systems won't survive 100 year run in countries with tens of millions.
Then, private healthcare is not the reason why Americans pay for it that much. There are lots of factors that drastically worsen the situation. People in the US are the ones who finance medical R&D, results of which are used by other countries relatively for free as individual American companies are forced to negotiate their contracts with governments. Which could be mitigated if American government would enforce for these countries to pay for their share in R&D.
Then, perhaps I am mistaken, but the US is the only place (or one of the few places) where doctors have to study twice to become doctors: first at regular colleges then in medical schools. It cuts out lots of people who could've been doctors, not to mention education costs.
Other thing that affects the costs is the fact that medical debts of individuals could be reimbursed by the government (the same applies to education). It creates incentives to actually make people go broke as insurers have nothing to loose in this case, but gain much more from the government which play along.