I can think of several reasons that shotguns of any variety are less desirable for home defense.
First of all is over-penetration. You want to avoid blasting through internal and external walls. A similar problem with high velocity or large calibers.
Second is barrel length. A long barrel can inhibit movement, make your actions obvious, and make aiming harder.
Third. In WWI, combat in the winding trenches was optimal with a pistol in one hand and a trench knife in the others, a combo that proved better than most others. And it has been noted that the narrow corridors of a residence are much like a trench with a ceiling. Over about 10 feet, the pistol works best; but if the enemy closes on you quickly to “smother” your pistol, you still are able to defend yourself with the knife (which in this case incorporated brass knuckles.)
However, once you leave the building, a shotgun is a far superior weapon, optimal for “backyard” ranges.
“Over about 10 feet, the pistol works best;”
Silliness. The more distance you have, the better that shotgun becomes. It’s power including a 20 gauge utterly eclipses any handgun you can think of, and it’s easier to hit with.
And in WWI, the shotgun was the king of the trenches.
Getting through a door is a little harder, but not much more so with a short barrel shotgun. But in almost every case, electing for a pistol over a shotgun is a pretty poor decision.