There are plenty of places on earth that have very little car insurance penetrations so we don't have to guess what that would look like. To me it looks pretty much the same. The major difference is that it's difficult to sue for liability and the people you're suing don't have much money so it's often pointless. Society just accepts that accidents happen, people die, and the survivors move on.
In these, often highly unequal societies, the people who have money have a lot of it so they in effect self insure.