No mention of the AR15?
Yeah, the AK is designed for “bottom of the barrel” expendables. Fine, dump it.
The AR15 isn’t - it’s designed for competent non-expendable operators able to afford cheap components like magazines.
AR15 vs shotgun?
30 vs 5-8 rounds.
Fast mass reload (push button (mag drops), insert mag, push button) vs individual loading (grab round, insert round, repeat 5-8 times).
Instant followup vs manual cycling.
Soft body armor penetration vs ...well, not.
Suppressable barrel vs no viable suppression.
Easy to carry more ammo vs ...well, not.
Shotguns are of course quite respectable for home defense.
Faced with the “brick wall effect” of capacity, I’d rather have 30 rounds loaded instead of 5-8, with another 30 easily shoved in a pocket and just as easily shoved in the mag well when needed.
You forgot to mention that although not as recognizable as the sound of racking the slide on a shotgun the sound of an AR 15 bolt chambering a round is quite terrifying to the average lowlife home invader.