I'd be willing to bet most wealthy people in France have occasion to pay out of pocket beyond the healthcare they could get for free from the government.
Yes, there is always something better that only the wealthy may afford-but that doesn't mean the baseline level of care for most people can't be improved. People don't expect the world's best surgeon to work on them.
And either way-the care for most Americans isn't necessarily better than Canadian or Swedish care, many rankings are significantly worse while costing the most.
I know one thing-if I had health care covered, I'd be more willing to start a business or take a break from work. That would make me happier.
To support this argument I cite real world scenarios where the difference between your loved ones living and dying could possibly come down to how much money you have.
Now if you're extremely rich you might be able to get a famous surgeon that middle class doesn't have access to, or get a new treatment only available in foreign countries, but at the end of the day I don't think it's going to have a huge impact on your chances of survival because what you get from healthcare is already really good.