Ever hear of an "uninsured motorist?" I even pay extra on my insurance in the event I'm hit by one. We still need to figure out how to make it not only affordable, but to get everyone's skin "in the game" so to speak.
Not saying it should be mandatory, but you can't walk into any hospital whenever you have a headache and demand an aspirin.
The uninsured should treated but their bill will be paid from a fund setup by the government. It will be considered as a loan and treated like a student loan. It can never be discharged unless fully paid off and wages (or government benefits) can be garnished to repay it.
An uninsured motorist is a criminal that is breaking the law. The reason we all pay extra on our policies is because we know that regardless of the law there will always be outlaws.
We pay so that if we get involved with an 'uninsured motorist' we don't get stuck with the bill.
Depending on the state and type of accident the 'uninsured motorist' might be sent to prison.