Most governments, and even most citizens, of developed countries want to ensure that everyone has access to some level of health care. From a purely pragmatic point of view, it is not in anybody's interest to have a lot of sick people walking around. Yet provision of universal health care presents other problems. Then there is a danger of too much government, spending too much of some citizens' money, in order to provide too many benefits to others.
Finding an appropriate balance is not easy. Leaving some people :"out in the cold" is unconscionable in a wealthy society. On the other hand, trying to bring everyone's health care up to an "average" level will likely pull down that average, while hurting everybody who is currently enjoying "above average" care. The answer probably is that a central government should spend SOME money on everyone's health care, but not too much.
The alternative could be "socialized medicine," where everyone gets more or less the same access to care; It will be presumed that "one size fits all," even though it doesn't. The result could be an overreaching bureacracy that dictates the types of treatments allowed, and favored (read, "cooperative") doctors to provide those treatments, whether or not either is in the best interest of a particular patient. It's enough to make a libertarian want to oppose government health care. "Better dead than Red."
Simply put, the problem with universal health care is the pressures that it creates for uniform health care. If the government is going to operate "some" (that is, more than a small part) of a system, there is a tendency for it to want to operate ALL of it. Health care is not different in this regard than other programs.
Still, provision of a bare minimum health care package should be the aim of government, just like the establishment of other "bare mininums" e.g, regarding clean air. (It might work like a minimum wage). Anything over and above that minimum should be a matter for the private sector to determine. That way, the government could have its way in the most critical instances, while most health care outcomes are still determined in the private sector.