Brandon, I disagree with your statement that "Somebody who overshoots with a shotgun won't come close to hitting anyone (intentionally) with a handgun." People who generally overshoot with a shotgun, don't place the butt of the shotgun next to their shoulder, instead they shoot from the hip and have the forward hand elevated slightly. With a handgun, people do not operate it from the hip unless the intruder/bad guy is RIGHT ON THEM and they are shooting immediately upon unholstering the weapon. Shotguns do have the distinct sound, and make a lot of noise, but a handgun is much more appropriate for home defense. Regardless, someone should take the time to train with the weapon they will use instead of simply purchasing a shotgun because they feel that it will be there when they need it.
I speak from my experiences as a boarding officer for non-compliant visit, board, search, seizure, and a weapons officer in the military.