it seems to me shotguns have been doing a fine job of home defense for a century or so...
Much of the shotgun's appeal was simply the intimidation factor. Especially prior to around WW-2. A shotgun could easily be effective by someone with little experience and even a couple of bird shot pellets could kill someone.
Not outright mind you. But with the medical care years ago what would be a minor wound today could easily get infected and lead to a long, slow, painful death days, or even weeks later.
No one wanted to die that way and the presence of a shotgun, even in the hands of an inexperienced shooter would diffuse a lot of disagreements.
We had female shooters in tears and leaving the firing line when attempting to qualify with the shotgun. Recoil was just too much for them
Typical 12 and even 20 ga buckshot loads are comparable to 300 WM recoil. Almost no one would recommend 300 WM for a novice hunter, but shotguns are often recommended for inexperienced shooters. Just something to think about.
A shotgun is definitely part of my HD toolbox. But INSIDE my home I still much prefer a handgun. There is no place in my home where a shot over 10-15' is possible. It doesn't take an accurate handgun to do that and I want to have one hand free.
Any long gun is more cumbersome than I want INSIDE, and a shotgun pattern is so tight at those ranges that a carbine would be just as effective. With less recoil. I wouldn't reach for it 1st, but indoors I'd just as soon reach for an AR carbine as a shotgun.
But if the action is OUTDOORS a shotgun with buckshot is the best tool for the job. The range is limited, but I could be effective from my home to my property line in any direction.