I come from one of those countries (Canada) and I currently live in New York. I also work mostly with people from Europe, whose healthcare used to be run by the state. All of us have "good" health insurance. I don't have a single colleague that would take America's health care system over the health care system run by the state they used to live in.
In the US, we have to chose between plans with deductibles or co-pays. Then, after getting a plan, we have to go to specific doctors or specific hospitals or we risk paying huge amounts of money. In Canada, I got a plan with no deductibles and no co-pays. Then I got to go to any doctor or hospital that I wanted to go to. Plus, while I would have to pay about the same in taxes for health care in both countries, in the US I have to pay for insurance on top of high taxes!
In Canada you get real freedom in health care, while in the US you get pretend freedom.