You're making the assumption that nobody could possibly pay for their health care out of pocket. That's just not true, even with health care as expensive as it is these days.
With the exception of the most wealthy (ie, Bill Gates), I guarantee that there is a health issue that would bankrupt you. Also, if you are that wealthy, why wouldn't you insure your health? It would be a pittance compared to your overall wealth and just simply a prudent thing to do. I bet you that Bill Gates and Warren Buffet have health insurance.