So you would rather have to have paid out-of-pocket the three times in the past 15 years for whatever happened?
In that 15 years, I paid somewhere on the order of $14-15k for insurance that paid me back less than $4k total. Worst investment ever. Hell, until I replaced my previous car recently, I paid more per year than the total KBB value of my car.
Now, do you have/want to pay all that money, or have the insurance company pay that money?
I would, grudgingly, put medical insurance in a different category than car insurance. Not to say I approve of mandatory medical insurance, and I still loathe the the insurance companies (if for a different reason, for having created an artificially hyperinflated market thanks to most people having a complete mental disconnect between the idea of treatment actually costing $400k vs paying $3000 or so out-of-pocket). I will accept, though, that we all eventually die and our last few years cost a small fortune in healthcare. We do not, however, all eventually get into car accidents with damages adding up to dozens of times the price of my car.
Or as you so aptly put it, "it would take you 400 years to recoup what the insurance company will be paying out" - The flip side of which means that such an accident happens at most once every ten driving lifetimes, and realistically far less than that (since that would assume 100% of all premiums paid went solely to that rare huge medical bill). Big scary numbers look big and scary, but that doesn't make it any more rational to live as though it will happen to me.
As for the potential liability issues, consider me a biiiig fan of "no fault" states - For that matter, the real topic at hand (driverless cars) will likely eventually force every state to go no-fault, since the question of who bears responsibility for an accident becomes effectively a battle between auto manufacturers, not passengers.
I do not like driving in states which don't require insurance
No worries! Your insurance company already charges you for "uninsured motorist" coverage, even though such things shouldn't theoretically exist in states that mandate insurance. How thoughtful of them to make sure you can rest easy!