I'm getting the impression that a shotgun is recommended because you can't miss with one. That's not true. Those big 40" wide patterns you see in pictures are shot at 40 yards. The longest shot possible inside my home is 21 feet or 7 yards. At that distance, the shot pattern is only as big as a fist. You still have to aim. The advantage of a shotgun is that it's easier to aim than a handgun and hits are more effective.
That highlighted sentence is a very succinct summation of this whole discussion about why to choose a shotgun over a handgun.
Gunnery, gunnery, gunnery. Hit the target, all else is twaddle!
