You can make the same statement about any insurance. Car insurers don't produce or fix cars. Home insurers dont build or sell homes.
That isn't what insurance is. Insurance is something that takes risks that you are not prepared to take. You could probably do without health insurance. But you are taking a tremendous risk in doing so. Some people take that risk. That's why there are a lot of uninsureds out there (there are also other reasons of course).
But insurers do not execute people, as your post implies. Nor do they drop people for claims, which btw is illegal in all 50 states. Nor do they increase premiums on people for making claims, which is also illegal in all 50 states.
But risk is a fact of life. That health care is expensive is also a fact of life. Health care is expensive for the same reason divorce is expensive: because it's worth it. Managing the financial risk of illness is what insurance companies do. ANd they do that better than the government is ever likely to.
You are right, the same can be said about any insurance, but health insurance is quite different that other insurance. First, everybody needs it -- because the underlying need is the need for medical care. The same cannot be said about all forms of insurance. What is at stake is totally different.
The other difference is that this type of insurance is more complex. When you destroy your car and other property in an accident, my guess is that the damage is more circumscribed. Health care, on the other hand, can be a never ending proposition (consider the recuring costs of someone needing constant medical treatment vs the cost of replacing a car or a building).
And anyways, in some places, some part of auto insurance is handled by the state at a much lower cost. For example, in the province of Quebec, government insures everyone for bodily injuries. Why? Because they calculated that the amount of money wasted on legal fees for bodily harm was so big that it was financially better to get everyone covered regardless of who was at fault, what coverage they had, etc. Trial lawyers aren't happy, but too bad so sad...
As for the risk you are describing, it's a risk that the rest of society has to cover, because unpaid medical bills are paid by everyone else. And since we aren't ready (yet) to let people die at the doorsteps of hospital, it seems better to just get those people officially insured. Plus, families having to go bankrupt for medical bills, because they took the risks you describe, still costs society as a whole.
Insurers increase premiums through all sorts of ways. Heck in the worst case they decide to cancel entire groups of policies like the company did in NY. Plus, you implicitely approve of this model where there are dozens and dozens of risk pools, when in reality there should only be one risk pool from coast to coast. What purpose does it serve that company X have a different risk pool than company Y?
I forgot a "Shabat Shalom"!