Interesting, maybe the laws are somewhat different in the United States (sorry, I'm assuming that's where you are from). As far as I understood over here, there are two parts.

The first party part (receiving damage) is optional as long as you own the car (you don't have to repay a loan if it is written off). The third party part is mandatory (liability), to cover the damage that you do to someone else. As I understand it, if both parties have both first and third party insurance, then the insurance companies will compare the difference and sort the claims that way, so one transaction rather than 4?

Apologies if that is what you were already saying! Also, I don't know how the laws work in the US! That said, maybe I should double check our own insurance to see if my understanding is correct or not...