It's usually possible "self-insure," too. Basically, you put up some amount of money (of order $30-50k) to the DMV as a surety bond. Then if you're held liable for an accident the state doesn't have to worry about you paying up because they already have the money.

$50k is comically insufficient to cover the damage you can do in a car in a single incident, though, and such a bond is a limp assurance at best.

I wonder if there should be a per-vehicle cap on damage where a vehicle is so expensive that the owner insures it for any damage over some amount, say $60,000, or the 95th percentile new car sale price.

Damage to vehicles isn’t the problem. The tail is hitting a car full of surgeons and ruining their careers so you are paying out gazillions in personal damage.