Health care is a good or service that depends on other people's labor. People do not have a right to other people's labor (no matter how much they insist otherwise). It's entirely reasonable to bring up the fact that most Americans are happy with their health care.
You can bring it up and it very well may be factually true, but it's irrelevant to the discussion.
Oh god not this nonsense "you're enslaving the doctors" argument.
By the way, insurance companies don't provide health care. They're a financial layer set to extract profit from those who need it, and United Healthcare seems to be the best at it.
As statistical multiplexing usually does, it improves things somewhat when you can't grow things larger, but when done for-profit with dividends, often disincents actually solving the capacity problem.
Racism is a lot like classism, though, and the distribution of health care is a consequence of structural classism of capitalist society.
I'm not sure what your second clause means other than "currently, people with more money can buy more health care". Of course it would be nice if the supply matched the demand r.e. health care. But neither single-payer systems nor more radical "restructurings" have solved that problem.