Problem with that is that it doesn't really work that well. The quality of care is so low and it increases taxes by such a large amount, that even in Finland companies provide private healthcare programs to employees. In Sweden, where COVID-19 is running rampant, a lot of people have gotten zero care. They look at the age of the person and if over a certain threshold give morphine instead that is guaranteed to kill them. In a perfect world yes, but I don't know if it could ever be realistic anywhere (with any degree of quality in the care). For life saving operations and such, even though prohibitively expensive, it's still worth it, but a 'free card' maybe not so much.
But this is off topic probably, my list was suggestions on real change towards making the society more equal, not a comparison of mixed economy countries vs capitalistic ones as this is turning into