Not a LEO (though I did once ride reserve with a small town PD for a few years), just an old redneck, retired librarian, former EMT and longtime bird and small game hunter who grew up with a pumpgun in hand. I've been shooting them for... a good while now, let's say.
So I choose what I'm good with for protecting Casa Lapin, what I trust to work for us. It happens I'm reasonably good with a shotgun (though there are some folks here who have dropped more shotgun shells than I have fired). It happens I carry a pistol whenever I have pants on as well, but given my druthers I'll take a shotgun for close in trouble that I know is coming or trouble that gives me enough time to snag one of several 870s tucked away here and there.
And if it happens trouble appears over a hundred yards away (not likely but you never know), there's an AR handy too.
You said, "In a close quarter combat situation it is next to impossible to miss with a shotgun(due to the pattern of the blast)."
It's not true. It's actually pretty easy to miss with a shotgun, especially at close range. There's a thread running over on S&T right now about a shootout in Denver where a shotgun-armed bandit missed a couple of cops at 12-15 feet, for example. I've seen it happen in training too, shotgun patterns close in are pretty small- and some stay pretty small for a pretty good distance. My HD guns will keep a full pattern of 00 buckshot on a piece of notebook paper at 25 yards, for example. The biggest defensive shotgun myth of all is that "you can't miss with a shotgun." You can, and people do.
So why do I prefer shotguns, when I have access to handguns and rifles and a reasonably good skill set with them as well?
Simple. A 12 gauge is .73 caliber. It fires projectiles that weigh an ounce or more (that's 437.5 grains, by the way) at velocities (given my chosen defensive ammunition) of about 1600FPS. I don't know of anything more effective against thin skinned lightly constructed critters up to 250- 300 pounds at close range than a shotgun loaded with buckshot or slugs.
With slugs (on board the gun in our case) the house shotguns are good out to a hundred yards or so. That's enough range for defensive use in almost any conceivable situation, even in rural areas like ours.
Defensive shotguns here are 37" long overall, with an 18" barrel and conventional stock with a 12.5" LOP. They are plenty short and maneuverable if it's necessary to go somewhere with them. More likely my wife or I will be bunkered down somewhere waiting for trouble to come to us, if trouble's inside the house. Maneuverability is a nonissue under those circumstances. As for disarms, good luck. Anyone who knows how to handle a shotgun in close will give you a new nickname if you mess with them- Stumpy.
As I and others have said before here- use what you're best with for HD. The question of personal and household defense seldom has an answer that is strictly limited to hardware. It's much more of a software issue, most of the time.
Stay Safe,
lpl/nc