Most countries with free healthcare do have woefully underpaid doctors. The NHS has been cutting back aggressively on doc salaries for years, letting them fall well behind inflation.

The only thing I can say in their defense is that at least docs in those countries don’t generally take on massive, private, un-dischargeable debt in order to do the job. In the US we treat the medical workforce as a public good, though they have to take on all the risk of entering that workforce through private financing.

I get to drive on most roads without paying, but I wouldn't say that the roads are "free"?

Compared to toll roads they are free...

We've uncovered a potential ambiguity in the original phrasing of "free health service". Could the now-dead response to that comment have been highlighting this very ambiguity?