I didn't mention the medical liability, since a modern civilized society shouldn't need to have me worried about medical liability. I was lucky to have good insurance when I was a pedestrian hit by an uninsured driver. I wasn't on the hook for my $60,000 in medical bills, because I had insurance. In a good society, I shouldn't need private medical insurance to protect me if I get hit by an uninsured driver.
Now, if my new car gets totaled by a shitbox '88 Cutlass Cierra driven by a person who can barely even afford THAT car, then that's where requiring insurance comes into play.