For all the hand wringing about universal healthcare and laments of "who will pay for it," the simple fact is, we have universal healthcare right now.
If a person in the United States collapses in the street and is taken to a hospital, it doesn't matter who they, citizen or immigrant, undocumented, uninsured, on and on, they will be treated.
They will be treated with the most expensive healthcare on this planet. It maybe too late to be of any real help, but it costs the same, without regard to the outcome of the treatment. The best part of this farce is that we all pay for it. In the tradition of the "there's no such thing as a free lunch" school of economics, the cost of healthcare to those who can't pay for it is squeezed out of the economy, one way or another.
This leaves the question, 'If we're already paying for bad and expensive healthcare, what are people bitching about?,
The answer is obvious. The objection is not to paying for healthcare, the objection is to good healthcare at reasonable costs. Since the greatest amount of this expensive and inadequate treatment is absorbed by the poor, the logical extension is, the real problem is supplying quality healthcare to poor people. It gets murky at this point, because it's difficult to understand the motives. Perhaps there is a belief that healthy poor people will simple result in poor people living longer and thus consume more wealth which rightfully belongs to rich people.
Personally, I think it's just a general dislike of poor people.
It's just unrestrained free-market greed. I don't want to be bothered by a rule change affecting my business and have to provide additional service or product when I can presently maximize my profit, so leave me alone.
But you bring up a good point, namely that there is a difference between having an accident or getting sick, and actual healthcare. Ideally, healthcare is something we do to ourselves and we only have an insurance policy because we know shit happens despite our best efforts. It should operate precisely like owning a home or an auto and having an insurance policy, but it doesn't.
With healthcare there is no obligation on the part of the insured to do anything to maintain the working condition of their asset, namely, their health. Therefore there is no way to control costs. Poor people are the least likely to be healthy long term. And as you say, if they have an accident or an illness they will get care, but it is a scary, bottomless pit to "insure" any asset unconditionally. Hence the reluctance to go full monty.
Is this one of those posts where you are trying to speak ironically, as if you are greedy free market capitalist?