These are not measures of efficiency. Medicare outlays are about 30-40% of private insurance for the same demographics.
> the care that people get from Medicare is substantially worse than what you get from private insurance
And this is, in fact, not true at all. US citizens on medicare beat their cohorts not only vs. other nations but vs. private insurance in the US too. Don't make the mistake of comparing your corporate insurance for a workforce with a median age of 30 with what retirees in the private market have available.
Retirees on the private market get completely shafted, though: almost everybody in their age group uses medicare, so the insurance will need very high premiums to cover their risks. From what I have heard, people who are on employer plans at that age have better health outcomes than retirees, regardless of where the retiree gets their healthcare.
I don’t think they are comparable. Medicare exists because private insurers refuse to cover old people at a reasonable price. It’s a good scam the private insurers have going: take peoples money when they are generally healthy and productive, drop them like a sack of shit onto the government’s lap when they aren’t.
That is why the life expectancy of the average obese, unhealthy American is about the same as the life expectancy of the average (much healthier) Japanese or European person. Americans are allowed to eat their way to an early grave and then have medical resources thrown at them to desperately keep them alive a few days longer.
EDIT: Also, I should point out that doctors generally demand a lot less end-of-life care than members of the general US population. They seem to understand that it is merely prolonging the inevitable rather than helping.
Basically, libertarians are just wrong on this. Government-run health care works great and we have many decades of evidence showing that.