Aside from the question of the logistics of "standardizing" on calibers/gages for firearms in a household, when looking at an extended family or mutual aid group, the idea becomes doubtful. "What? You have a 16 gauge shotgun? That's it, you're out of the group!"
Well, the context I was addressing was more of an individual situation, like like Mr. Bill, who didn't have several different chamberings. There just isn't a compelling need* for 20ga in addition to 12ga, or vice versa. A second 12ga (same model, two is one, one is none) is pretty compelling IMHO.
As to a MAG, if everyone keeps their stuff separate, fine and dandy. But if ammo and arms are kept together and accessible by various folk of various levels of knowledge and attention to detail, well, I think your kaboom exposure goes up, not down.
As to the need for a spare gun to shoot scavanged ammo, if it comes to needing to shoot scavanged ammo, I would think scavanged single-shot shotguns would be available as well. (I could see an argument for having rifles
in alternate chamberings, with preferred sights, sighted in, known condition, etc., but shotguns, especially single-shots, aren't precision instruments.)* Depending, of course, how one defines "compelling." I don't have a "compelling" need for a .44Mag lever gun, but it sorta fits. To each their own.