Poland, and we gave up socialism ... for the most part.
What seems to work the best is the combination of private and state options, where you can go to a private university, or private clinic, or private dentist (I certainly do), but if you're in a tough situation (as I was right after attending state university), you have a "free" option to fall back to.
The problem in medicine is the psychology, the moment you can walk up to someone and say: pay this, or that, or you _die_, you get 200$ epi-pens - same ones you buy in europe for 5$.
People will literally pay all the money they don't even have to save the life of theirs, or their family. At the same time people who are to poor (at that moment), to get help will suffer needlessly, and skip a prevention which is always much cheaper then curing disease that already spread.