Police generally don't arrive to break up assault/battery due to an accident. They generally issue fines. Most people exchange insurance and take photos. Yes, the police may act as pseudo-judges for the insurance company. I had this happen to me when I was not at fault but the at fault driver and his friend both lied to the cop, which ended with me getting the citation. The cop said it was 2 against 1 so he had to go with that. Hiring a lawyer would have cost me more than the ticket and the claim so I just bit the bullet.A little naive; rightly or wrongly, the insurance companies will very often apportion liability to the party the police find at fault, otherwise it's often knock for knock, which penalizes innocent parties.
Would you like them to attend after someone's beaten or shot as a result of the 'whose fault was it' argument ?