This is why I like our Socialized Car Insurance in BC, Canada.
Everyone has same insurer.
The prices are set and you have a discount based on years of driving.
You get in an accident, you send details in online, as does the other party.
You both get your car fixed.
If its not a massive accident with severe industries, you don't even call the police...they don't come even if you did, because there is no need.