Good friend has a Mossberg 500 with a pistol fore grip and pistol rear grip. It's fun outdoors for hip shots, and hitting water jugs. I NEVER would do that to my 870 Express Magnum.
I can see the mobility and SD applications, but I can move just fine around halls and doors with my 870 and all I've added is an ATI adjustable rear stock. When fully retracted it provides a very compact package with the stability of a shouldered shot, and ability to have no trouble in target acquisition with increased probability of hits. Especially if using shot instead of slugs.
Accuracy with a pistol grip goes way down from the hip, or off stance, unless you practice. My shots with the pistol Mossberg all were high until I "dialed it in". I guess in a household, across a room it would work, but you better have a good grip on that thing, be healthy with strong hand and arm strength. I'd rather know most of the shot is on target than having to "guess" in an SD situation, with adrenaline, and a host of other factors...that a pistol grip makes more difficult.
Just my humble opinion. Looks great in movies. But I don't find them applicable for me. My Stoeger Coach's 12g is even shorter, and is usually the one available as my last resort firearm. That is after, my handgun, and a reload aren't enough.
They are great for blowing up watermelon and water jugs!!

FWIW.