The ‘shoot to kill’ theory doesn’t have a place in either police self-defense or citizen self-defense. If you are faced with a threat, your goal is to stop that threat until it’s no longer a threat. If that means the bad guy is on the ground with his hands out to his sides, that means no more shooting for you until something else happens, like the bad guy reaches for a weapon.
The female officer in the video below, after her partner literally hit the bad guy with his car, showed restraint at first against an armed man with a gun. He’s definitely a threat and even after she shoots him, he continues to advance towards her and continues to try to get his gun to a usable position to shoot her.
The officer ends up firing a total of 20 shots, because his bad guy just wouldn’t give up. He continued to be a threat until the very end, and that’s why her use of deadly force x 20 was absolutely justified.