Public pay health care cannot be based on the principle of "compassion." Too often "compassionate" public health care relies on a careless individual suddenly making better health choices. But it is wise for the public to pay for care that has direct public impact. An example is controlling contagion. The power of government is the type of power which could contain and treat victims of an outbreak of influenza, plague, cholera, and other highly contagious, serious disease.
Sickness that is entirely due to personal behavior should not be a public obligation. If I eat too much fat in my diet and have a heart attack, I should pay for it. If you break your leg skiing, then you pay for it. If someone get a disease from ill-advised sexual conduct, that person should pay for it.
Private pay for private sickness has some very positive implications. First, most personal behavior is based on personal choice. Personal freedom is very important. But if that choice is unwise and results in disaster, it becomes a learning experience. The learning is not limited to the person who made the stupid decision, but anyone looking on can see the results, a public good. No smart aleck remarks about fatal learning experiences will be tolerated. Government still can't bring people back to life.
The second point is that assume we allow the public to pay for the results of a privately caused private health disaster. That is effectively a transfer of public resources to a private person. The equivalent idea is: Suppose I decide I must have silver dinnerware, because silver is antiseptic (and it is). I loathe germs, so I get nice dinnerware and enrich myself, and I can get the rest of you to pay for it. Yeah, not likely.
Okay, you say, but wouldn't it do the public good to exercise compassion. Everyone will feel nicer if we do, right? I won't go into the facts about the thousands of private health charities and churches doing this already. If the public government steps in, the problem is in the administration of care.
The "public" decides such matters by delegating the decision making to bureaucrats. That only ensures that poor decisions will be made. People who have little to do with the actual suffering will decide what gets treated and when. The historical fact is government bureaucracies have always been really bad at allocating resources. If the goal is truly the best health care for the most people, most health care should be left in private hands.