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.
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.