the idea of the SHTF scenario, if only for a mental excercise, is to prepare yourself for the unlikely (I hope) possibilities.
You have a lot of options using a shotgun, slug, buck, smaller shot, even less-lethal and rock salt sort of stuff (belive me, it works, - ounch!). But the shotgun has a limited range, even with slugs, that can be topped with a rifle, It and the ammunition tend to be heavy, and most of them not being magazine fed, they can be slow to reload. Shotguns are not the "Death ray" movies portray them as. But as Bob Olinger (Billy the kid victim) would attest, in the right circumstance, nothing else will do the job so well.
Shotguns can be visually intimidating, and as to the "rack rack" that supposedly make harden felons turn to puppies, I can't speak to that, but you've gotta arm it anyway. The "fan of shot" makes aiming easier in stress situations, and the utility of the shotgun makes it more user friendly to less experienced shooters.
Wyatt Earp's posse, in 1881-2 supposedly carried rifles and shotguns on their horses (greater tactical flexibility) I like the earlier comment that life is a long 3-gun match. The shotgun can, and should be an indespensable part of that.