alt Hacker NewsIt's more about making a fair assessment of whether servicing a market via private or public enterprises is more or less efficient. What you mention is a comparison between different markets, not a fair comparison of the same market run either publicly or privately. Health care insurance companies definitely "tax" you for their inefficiencies (through higher costs) and they are definitely something you "need to do business with".
The classic "government can't do anything right"-trope is quite strong and influences voting and policy making. My hypothesis is that the reality is closer to "cooperating with many many people in big organisations is very very hard to do efficiently".
Health insurance is so regulated and so intertwined with public policy aims, that ostensibly private health care companies are themselves essentially an arm of the government. Indeed, the fact that I "have to do business with" them is itself a consequence of particularly-complicated government regulation. The American health insurance system is one of the most unpleasant (sets of) bureaucracies I personally have to deal with, especially because I have changed jobs a lot recently which entails losing and then regaining employer-benefit insurance (which itself really annoys me - I wish I could just pay for ordinary health care in a way completely unrelated to my job and that my job had nothing to do with). I don't have a grand theory of how best to reform the entire American health insurance system, but I'm in favor of doing so; and I suspect that a better system would look a lot more like removing the insurance component of it in more contexts, and having more medical procedures paid for out of pocket at point of use by ordinary people - which is something I try to do right now anyway when I can.