One problem among many is that US police are both allowed and trained to use deadly force very quickly, when under any kind of threat. German police will often (successfully!) shoot to disable, not to kill, even when confronted by someone armed with a knife. It's a common American meme that when police fire a gun, the only rational decision is to shoot to kill, but it's just not true.
From what I've read very few police officers have the time to selectively shoot someone. If deadly force is called for, you aim for the center of the person.
Also, shooting to injure rather than kill is not exactly easy. If you take a bullet in a major artery in a leg or an arm, you can bleed out just as quickly as a bullet to the chest.