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...
You are correct in your assumption that I am from the US. We have a similar system were if you own the vehicle you can drop the portion that covera user caused damage and only keep the liability portion. However I am speaking in a more broad, conceptual sense that insurance should be a choice not compulsory. I am firm believer that individuals should be left to their own devices to make choices that they deem best for them without interference from government and with the full responsibility and consequences of their actions. Rights as citizens are infringed as government takes choice away in the guise of public safety. Regulations dont make us safer in the long run, having the faculties to make informed, educated and safe decisions on our own is the way. Education not regulation is the answer.