It's not that shoot to kill is the only option, ever.

It's that center-body-mass is the largest target to shoot at, and therefore the safest to shoot at in a public area. Safest for everyone except the one being shot at, that is.

God, does that make sense? It's hard to explain that. You want the largest part of the bad-guy to catch the bullet, to make sure the people around him don't. Therefore, shooting at the (relatively) stable center of his chest is a heck of a lot easier and safer than shooting at his moving arms or legs.