On definitions of "socialism"... I think any country that transfers wealth from production (has tax) and uses it for public services has a sliver of "socialism". That these tax-funded public works can help the economy is textbook Keynesianism. It's at least socialist-adjacent. All countries in the first world have some of this, even the US.
Not to open up the health care debate, being Canadian, I'm happy with our system of federal mandate to provide it, but letting the Provinces figure out how.
But I am sympathetic to the arguments of my "right-wing" American friends. They would pose the question, should health care be a "right"? In the same sense that free expression is a right. I'm not sure.
The reason I'm not sure is... as technology improves, health care seem to get more and more expensive. Like a reverse-silicon transistor effect. What happens if the technology existed to extend the life of any person, no matter how sick, but at a cost of $1-million per-day? We could keep everyone alive, but at a cost that would quickly bankrupt any nation?
I think before health care becomes a "right", something needs to change in how cost is sorted out. I know drug patents, genome patents are a hot issue that I know very little about. But, something would have to change to reduce the long-term costs for the most vital health care. I'm not sure why health care procedures don't reduce in cost over time, like last generation's console gaming system does.