You can get a cheap (like $10) EU-wide health insurance with wide coverage, or get a refund from your country after getting healthcare in another member country

You can get a cheap (like $10) EU-wide health insurance with wide coverage, or get a refund from your country after getting healthcare in another member country but it's quite the bureaucracy. (That's where the insurance company helps.) Now even if paying from out of pocket, the cost is unlikely to bankrupt you. The expensive things are experimental biological therapies (e.g. new antibodies) and some cancer treatments. As for quality, it depends, e.g. Poland has the healthcare starved for money and qualified people. That's because it's way too small bit of GDP. (I think around 5%.) That mostly makes specialist care much slower, not the general care, and hospital workers overloaded. Cost cutting is visible everywhere. (Only Romania and Bulgaria are more starved.) It's still much better than US situation. As a number, it is around 700 Euro per year per capita. And the money is supposed to increase to some 6% gradually.