The most efficient, lowest cost health care system may result in millions of people without coverage. Just like it does for cars, to use your example. To get coverage for everybody would mean a less efficient system.
Now we can argue whether an efficient free market system or an inefficient government coverage is "better." But I wasn't arguing with that part. That's a moral/values argument, not economics. I was arguing about how you knock the "free market" system because our private insurance system doesn't work. Of course it doesn't work. It is not free market. It's a mish-mash of different ideas in different states with nobody knowing what's really going on and the doctors having to hire legions of administrators to keep it all straight.
Are you arguing that a more socialist health care system would be better than what we have now? If so, I wouldn't necessarily disagree. But I would argue that a true free market system (or a system than leans very heavily towards the free market, since the government will always have some say) would be better than what we have now and would be better than a more socialist system.