Once he was out of his car, and in his home, they should have stopped, cooled themselves down - adrenaline from being in hot pursuit can lead to rash decisions - seized his car, and then decided whether it was worth the while to attempt to arrest him for running the stop sign and fleeing. It might have been better to have, as I said, seized the car, then gone, filed a report, obtained an arrest warrant, and then followed him and executed it at a later point in time when they would have the element of surprise.
Unless the car was stolen, seizing it is going to put much more of a justifiable hurt on him than trying to arrest him while the adrenaline is still pumping.
