Your point about anecdotal evidence is fair enough, so let's look at statistically-meaningful data gathered by the most reputable source on the subject. According to a 2004 report by the
Institute of Medicine of the National Academies of Science:
"Lack of health insurance causes roughly 18,000 unnecessary deaths every year in the United States. Although America leads the world in spending on health care, it is the only wealthy, industrialized nation that does not ensure that all citizens have coverage."
You cannot ask for more accurate data, from a more reputable source, which is more damning of our system compared to all other wealthy nations where ZERO people die unnecessarily every year due to lack of coverage and they pay less for it, too. Evidence just doesn't get much more compelling than this.
For the record, no one is saying that there aren't people in this country who have great health insurance and great experiences. If we had no public schools, if our education system was ONLY private and 50 million couldn't afford an education for their kids, there would still be plenty of people in this country who would get an excellent (perhaps pricey) education. That's beside the point. Like free public education, we can have free public health insurance and people can keep their expensive private stuff if they want.