No, it can't, because in a totally free market nobody would have monopoly rights to produce particular drugs or provide particular treatments, so if one provider tried to charge a price nobody who needed the treatment could afford, they would go out of business. If it proved to be impossible for anyone to make the drug or provide the treatment at a price anyone could afford, then that would be a failure of the free market, yes; but it's an extremely unlikely failure mode as compared with the much more common failure modes of government granted monopolies and government determined prices.

That said, in a democratic country if the majority shares your risk preference, then that majority can vote for politicians who will enact it:

> I would rather prefer that the government took this risk on my behalf of me and just charged me a flat rate throughout my life.

And that would be a form of cost sharing, which I mentioned--all taxpayers share the costs of expensive treatments, on the assumption that only a small percentage of them will actually end up having an illness that incurs those costs.

However, that still only protects you on the assumption that in fact only a small percentage of people end up having the costly illnesses. But the illnesses people are generally worried about with respect to high costs--cancer, heart disease, arterial sclerosis leading to a high risk of stroke, liver disease, kidney disease, diabetes--are not that rare. So either we keep paying more and more taxes as a higher and higher percentage of people have the illness, to the point where we are just as badly off as if we each paid our own costs individually, or many people end up not getting the treatments at all because there isn't enough money to go around, so the risk you thought you were offloading to the government is back on you again.

This scheme also ignores the possibility of making the treatments cheaper. But the way to do that is to allow free market competition; we don't have that in the US since prices are not set by supply and demand but by a combination of government agencies and private health insurance companies.

> In general there are some things where government intervention is needed. Police, Education, Healthcare and Pension as these things cannot have a totally variable cost decided by a free market.

This is not the obvious truth you appear to think it is. It is an extremely strong claim which is not at all clearly established by actual historical evidence.

Lets be realistic here. What happens is that most drugs are either actually manufactured overseas or at least can be shipped from overseas for pennies. However due to regulations and lobbying drug companies charge really high prices for the same drugs and they make sure it is illegal to import those drugs. In case the government itself was paying for these drugs it would be much harder for the companies to game the system like this and an individual would be protected from such predatory practices.

> So either we keep paying more and more taxes as a higher and higher percentage of people have the illness, to the point where we are just as badly off as if we each paid our own costs individually,

This is not true if you observe the tax rates in any countries with government funded healthcare. The taxes more or less remain the same but of course there are differences in the healthcare budget.

> This scheme also ignores the possibility of making the treatments cheaper.

Once again the healthcare costs in the US have actually risen quite significantly under the private system.

> This is not the obvious truth you appear to think it is. It is an extremely strong claim which is not at all clearly established by actual historical evidence.

Police and education it already is true even in the US. Even pension has significant regulation. The only reason healthcare is not is aggressive lobbying by private companies.