If you have ever been in the position where insurances negotiates fault, then you would rather have your day in court.
My wife got in an accident a few years ago before we were married. She was driving down a two lane road, and I was in the passenger seat. The car in front of her was hit head on by a drunk driver. The force turned the car in front of my wife side ways and stopped it dead in its tracks. My wife swerved into the turn lane to try and miss the car, but there was no room to go anywhere . The insurance of the drunk girl determined that part of the wreck was my wife's fault and they were not going to pay for her car repair and tried to get my wife's insurance to pay for part of the other persons repair. My wife's insurance fought and said no she wasn't at fault. My wife's insurance didn't raise her rates because they didn't consider her at fault. The wreck went on my wife's insurance record as at fault. Then her insurance went up quite a bit, and she found out she couldn't change insurance for 3 years because every other insurer viewed her as at fault. Since it is insurance, there was no recourse to fix things.
In those cases you can go to court but in most cases it is settled between insurance agencies and fault is not so convoluted. Sure, they try to place blame on the other party but that is what each party's insurance company's subrogation department is for, they are there to fight fault on your behalf. You are suggesting in every accident everyone go to court to settle their dispute. So how do suppose the court system is going to handle that many insurance cases and who is going to afford a lawyer for all of their cases?