shotguns do have more stopping power than your average handgun, but your other points are not really true. even with no choke, the spread from a shotgun at home defense ranges is negligible. you still have to point it directly at the target, though this is a bit easier with a longer firearm. ammo you would choose for defense against humans (ie, buckshot) will easily penetrate one or more walls in a typical dwelling.
the short barrel and relatively low power of a handgun does make it an inherently compromised platform. but the short barrel does have one big advantage: it is much harder for an adversary to take control of the weapon at close range. soldiers sometimes transition to their pistol when clearing structures for this reason, although this is less common now with short-barreled rifles.
but at the end of the day, the "best firearm for home defense" is the one you know how to operate and feel most comfortable using. if they train frequently, you should absolutely take them seriously.
the short barrel and relatively low power of a handgun does make it an inherently compromised platform. but the short barrel does have one big advantage: it is much harder for an adversary to take control of the weapon at close range. soldiers sometimes transition to their pistol when clearing structures for this reason, although this is less common now with short-barreled rifles.
but at the end of the day, the "best firearm for home defense" is the one you know how to operate and feel most comfortable using. if they train frequently, you should absolutely take them seriously.