Frangible 5.56 will stop any threat in the house without shooting up the neighborhood.
Shotguns are betting on one or two intruders, who are hit amd incapacitated while you reload.
And, if the intruders have ARs or AKs, they can retreat out of your range and still fire on you with effect.
Point being, shotgun for urban? Maybe. If you live in a nice urban neighborhood where the home intruders promise to come in groups not more than two.
Rifle or carbine for suburban? Probably.
Rifle or carbine for farm and ranch? A certainty.
A gunfight must be won to worry about the next gunfight, so having a carbine in the safe downstairs and a pistol in the bedroom doesn’t make sense to me either.
Around here, it's usually at least 3 guys with guns who kick the door in the middle of the night, which suggests having way more than 6 or 7 shots available.
As far as shotguns, I watched a guy pattern a Benelli M4 a few years ago, at about 30 yards, with 00 buck. The pattern was only about 6 inches, so "scattergun" did not apply. YMMV, of course depending on gun, chokes, and loads. So you'd still have to aim it roughly as well as a rifle, under duress. More recoil & fewer shots on board. So, I keep an AR handy.
One of these days I might get a bullpup shotgun perhaps a Tavor or similar, which helps the ergos.
