[legion]

I think there are two different use cases here:

1) House Clearing

IMO, a light mounted on a handspoon is best for this job. Small, maneuverable, and if you can see the bad guy, you very nearly have sights on him. Here you have the ability to fire multiple shots rapidly. Sure, the sound of racking a shotgun will cause some criminals to flee, but not all. Some won't recognize what is going on. Some might be high. Some won't care.

2) Shelter in place

In this case, you know someone is in your house and you think they are coming for you or your family. Someone is on the phone with the police. Having a shotgun pointed at the door in case they breach is not a bad defensive posture. I'd want to be something like 45º off from the door in case they decide to fire through it.