Actually, I shoot USPSA combat handgun competition and police officers are not nearly as good of shooters as they are portrayed to be. They often come in to shoot with us and I think many of them just get scared off. They are always tactically competent but they are somewhat clumsy and inaccurate.
Most police shootouts are won by the police because the police have a understanding of the basics of armed combat, and their adversaries almost always have none. Against a tactically educated adversary determined to kill them, most officers don't stand a chance.