It would also be cheaper if it were truly ubiquitous and single-payer. The prices European hospitals (even the private ones) charge to the various national health systems are a fraction of the list price for the same procedure at the average American hospital. It's only the current insurance system in America that creates perverse incentives to inflate list prices to the ridiculous levels we're accustomed with.
Which is why you will now pay a tax penalty if you don't pay for health insurance coverage. What contributions you make to society is part of a contract, not a unilateral choice.
If, when the care required to save your life cost above, say, $10k in one year, you agreed to die -- then I would consider you to be taking the notion of individual responsibility seriously. As it stands, you are proudly forcing the rest of us to bear your risks.
Personally, my choice is dictated by an attempt to understand my body and live a fuller life and some of those attempts suggest to me that insurance is overrated in light of Bayesian reasoning. -- not to suggest i actually sat down and calculated, just a guess.
For example, consider what happens if, as is very likely, you change your mind. The doctor says, "It's cancer, but it's treatable." You say, "Oh, I didn't think this through, please save me."
Very few doctors could say, "Tough, here's some aspirin, GTFO." If they could, they wouldn't have chosen to become doctors.
Or consider the case where you're unconscious and dying. Do they save you, or not? They can't really know what it will ultimately cost, and the certainly can't know how much money you could raise.
Then there are things like contagious diseases; you would have to spend money enforcing some kind of quarantine in order to cater to the "opt-outs".
For all other cases, like most types of cancer -- you can opt out -- only you'll have to commit suicide (I don't advocate this either).
That said the insurance system in the US is too broken and needs to be scraped.
If insurance weren't ubiquitous, service would be cheaper, sure. And people would die or be bankrupted by treatable medical conditions like crazy. This is why insurance is so common. People don't like that kind of thing.
Given the system that we're in, you're doing me no favors at all by refraining from obtaining health insurance as a healthy person. You've decided that the risk of bankruptcy is acceptable while externalizing a lot of that risk.