Some people can afford to pay for health care coverage. Some people can't. That's the dirty secret of the health care debate.
Ordinarily, goods and services are directed to people who can pay for them, and denied to people that can't. But this is HEALTH CARE we are talking about. Lives might be at stake!
If we want "universal" health care coverage, what we're really saying is that we want to provide such coverage to all people, some of who can't pay for it. Then we either have to make up the difference from taxpayer funds, or "skim" money from people who are paying for their own health care coverage, via an "insurance" mechanism.
Of the two options, taxpayer funded health care is by far the lesser evil. Public health is a public good. If some poor person gets, say, tubercolosis because s/he can't pay for health care, that increases EVERYONE's chances of getting the same disease. People in poor health also have more accidents, industrial and "civilian" such as cars. Therefore, it makes sense for the "government" (read the taxpayer), to fund some minimum "standard" level of health for everyone.
The situation is different with "private" health insurance, which is what most people buy.. HMOs and similar organizations are unpleasant to deal with. They do, however, have the advantage of telling people how much things REALLY cost. They can be fine if people are allowed to "opt out" of them by not using them, and instead fully funding their own treatments. The problem is, HMOs require something called economies of scale to function. The more doctors AND patients trapped in the toils of the programs, the more "efficient" they are likely to be. So they have NO interest in allowing people to choose their own health care programs. That would just result in fewer profits.
People who can pay for health care should get the best health care they can afford, independently of HMOs or other insurance organizations. People who can't pay should get the health care that taxpayers say they can afford. In no event should the two groups of people be "mixed" within the health care system itself.