The delivered energy at the defense ranges considered here are greater than a .357 Magnum revolver cartridge, but the longer barrel and greater weight of the shotgun results in less than half the noise and recoil. Of course home defense means more than defense against two legged creature. In any breakdown of civilization, a weapon like a shotgun becomes critical. Pet dogs are abandoned, join in packs and quickly become feral. The can, and do, attack domestic animals, pets, and are even a danger to children.
Racoons can get into a chicken coop and kill a flock very quickly.
Rabid dogs are not uncommon in a societal disaster. These must be dispatched quickly, yet they are a moving target and hard to hit. This is where a shotgun really shines, as the pattern of shot is easier to put on target than a single bullet fired by someone shaking under extreme anxiety and stress, and repeat shots are more likely to put additional pellets into the target zone. Hunting for food may well be necessary in the future. One lonely .410 shotgun will not suffice as complete home defense against a determined band armed with AK-47's.