Because in fact shotguns are an incredibly useful thing to have. With buckshot they are a well proven one shot manstopper on unarmored enemies, and then you can use slugs, rifled slugs, and saboted slugs to extend your reach. Then you can put in neoprene shot or foam slugs, or CS gas, for riot control. And when a door gets in your way pop in a frangible breaching round and let fly. In alternative timelines presumably they have practical flechette and explosive/incendiary rounds too.
Shotgun isn't obsolete. It's a swiss army weapon. Simple smoothbore delivery system to solve whatever problem it is you're having.
I never use em'. Well at the start a bit. I don't use em' anywhere and Fallout is not my prime game by a long shot. I don't use em' in Stalker where there are many fine shottys. It's a hunting weapon for killing birds.
Bring your shotty, I'll kill you long before you are in range. Run out of ammo, a real assault rifle, Stalker style, reloads 30 rounds in a couple of seconds. A shotgun is going to take a quite while and there will only be a few rounds when you are done.
If the world is not too dangerous, FNV, shot guns can be fun. In a dangerous place they just get you killed. I die once in a while in FNV but I don't think a shotgun has ever been the cause. hardcoe very hard. Anything less is ridiculous.
Oh and never VATS. Good lord.