For home defense there are a few things you should consider......First and foremost is do you have a family that lives with you? If you do a shotgun is a terrible defense weapon since an intruder could very easily get a family member of yours in between them and you. In this case I'd much prefer an AR with a laser sight.
So you think it would be safer to use an AR which will go through a bad guy and then a wall hitting God knows what on the other side of the wall? Ever stop to think about that?
A load of birdshot in a full choke will not have much spread in the distances found in the average house and won't have much energy left to shoot through a wall if the pellets get through the bad guy. And if you think a load of #4 or #6 shot won't be devastating at 10 yards then You've never really played with it. Nobody is walking away from a chest shot of #4 or #6 shot at 30 feet and it is a whole lot easier to really smack someone with 200+ pellets than the 9 or 12 pellets found in a 00 Buck load. Remember this is self defense, not deer hunting.
9mm with the proper load doesn't have this problem you are describing IME. You have your own conclusions and there's nothing wrong with that. Just attempting to add some friendly ideas here
Good bullets properly placed always work, but not everyone knows what good bullets are, or can reliably place them in the field
