In Ca., the officer would have likely arrested the driver for being unlicensed and then booked him as he had no valid identification. That way they could run prints and verify his info.
And also would have given him an additional charge of driving without proof of insurance at the scene of an accident.
They would have also towed the car with a 30 day impound for being uninsured. If the owner of the car is other than the driver, the reg owner could contest and receive a hearing to get car out of impound early.
This is in certain cities, not all of Ca. Oakland for instance, where the cops are literally responding to murders and shootings everyday, they wont respond to accidents if there are no near life threatening injuries.