Let me start with the technical line: police do not "shoot to kill," per se. Police training stresses "shoot to stop." If they did shoot to kill, they would shoot for the head (which some particular specialized units do train to do in situations like hostage-taking). Generally, police are trained to shoot for the chest, which happens to be the largest target on the human body that also has significant blood vessels.
By aiming at the largest target, you make it more likely that someone shooting will hit. Hitting even a torso-sized target with a handgun is no easy task when adrenaline is pumping and someone is shooting back or coming at you with a knife. And a dirty little secret of policing is that not all cops are great shots. In fact, quite a few probably only fire their weapons when they have to for qualifications. Makes some sense- of all the things we ask police to do, shooting people is the thing that takes up the least of their time. Most never have to do it.
I mentioned blood vessels- a drop in blood pressure is one of only a few ways to render someone incapacitated (although it rarely happens immediately). People have gone through and won gunfights after being shot multiple times- one was a woman cop who was shot in the heart with a .357 magnum. She went on to kill the guys who attacked her before she collapsed. That's one reason suspects sometimes get shot a bunch of times- a cop shoots them and, because it's not the movies, pretty much nothing happens. So the cop either figures he missed or decides to keep shooting until the guy falls down, which can take awhile. I could go through a few cases where people have been shot many times, including through the head, and continued to fight.
Other ways to drop someone include a disruption of the central nervous system- i.e. a brain shot or hit on the spine, and bone breakage. If you shoot someone and break their femur, for example, they will probably fall down. So why not do that?
Well, a few reasons. First, if they have a gun, they can still shoot you. But even if they just have a knife, it's pretty damn hard to hit the femur or even the leg of a moving target. Shooting someone in the pelvis is actually a viable option, but going for 'center mass' is just easier to train and rely on. Also, sometimes someone who has been shot in the torso will just decide that they are supposed to lie down due to the psychological effect.
Incidentally, because someone can bleed out extremely quickly from being shot in the leg or shoulder, there is no legal difference in force between shooting someone in the limb or chest.
So the torso it is. And, unfortunately, the drop in blood pressure that causes someone to no longer be a threat also tends to cause irreparable brain injury due to ischemia if advanced medical care is not provided immediately. Which it usually isn't, unless someone is smart enough to be shot in the trauma ward of a metropolitan hospital.