Lots of countries have a better national health service that provides health care to all of its residents.
The funding will vary, but examples include Germany, France, Belgium, South Korea and Japan.
In Germany, for example, you just present your card whenever you get health care. It looks like a credit card, but the insurance pays. You don't. Everyone has insurance cover, including unemployed people. Also, pre-existing conditions are always covered. Insurance payments are taken from your salary and your employer also contributes. If you earn a lot, then you are in a different system, but to be honest the basic one is fine e.g. you can go to specialists directly, no waiting lists etc