I mean...I'm Australian. Of course it can be done, there are plenty of places already doing it. But it's not about being 'done in capitalism' or 'done in socialism'. Those are ideological window dressings. It's about providing quality healthcare to citizens.
Australia is not what you'd call a socialist country, is it? But we have far more social programs...and incidentally our health system runs at a far lower cost per capita. If you don't like our model and mix, there are plenty of others to choose from, most of which are cheaper than the US model, and lead to better objective outcomes in terms of healthcare.
I lived in Australia for a bit. Don't tell anyone I was an illegal alien. I was impressed by the schools, the welfare, the health system. And, at the time, the government was able to balance the budget. Housing was cheap, but what the hell was it with sneakers? I felt that if I wanted to buy a pair of sneakers I'd have to take out a loan.
My wife has family that lives in Sydney. That was back in '95. I don't know how things have progressed but I think I've heard they no longer are able to balance the budget.