My yard sign reads: Damn The Dog, Beware of Owner
While the right dog certainly has it's place in security, I'm not going to 'depend' on one for mine.
You display a vast ignorance about fire arms.
A stock hunters shotgun won't spread to hit the entire wall from across the room, unless you have one sawed off (illegal) to a 10" barrel. And with a 10" sawed off shotgun, you better be muscle-bound strong to control the blast/kick that it produces. The spread at 20' would still not cover the entire wall, but it would be good enough for your directionally correct claim. With a standard barrel shotgun and #1 buckshot, the spread won't be more than 3-4" so only very slightly better than a rifle or pistol.
And your average shotgun doesn't have a 10-20 round magazine to feed it, you have to stop to reload.
An inexpensive 12 gauge Mossberg pump shotgun with a short stock pistol grip is a decent gun for home protections, but it's not my first choice, and you'd damn well better practice with it and understand which ammo to use for each intended application.
What anyone needs for home defense is a firearm that they practice with and can control, well enough to hit a human sized target from 20 feet. I and my friends/associates can do that with any gun we own.