Because, unlike the cerebral onanism of gun fetishists, not everyone goes around their house packing a long gun in one hand and going through life with only the open hand to do something.
A gun you have ALL THE TIME is worth a lot more than a gun you don’t. And no one other than someone wearing a sling is going to have a shotgun on them all the time.
Home invasions don’t happen at times convenient to the occupants of a house. People like the subject of the OP aren’t going to “live the tactical lifestyle.” She’s old(er) and she’s not about to start pie-ing the corners in her home, she’s not about to start waving a long arm around inside her dwelling. She’s an older lady. She wants something that is going to inconvenience her the least. If it’s inconvenient, it WILL be left in the bedroom. That’s the fact with the person in question.
This absurd idea that a shotgun is the “one size fits all” solution to home defense is some of the most specious nonsense in the gun community. Especially the idea that “you don’t have to aim.” The next is that the pump shotgun is the best. I have all manner of shotguns - and my choice if I’m using a shotgun for home defense would be a semi-auto. The semi-auto action soaks up a bunch of recoil and “it just works.” You don’t have to remember anything. Just take off the safety and start pulling the trigger.
They most regularly happen at night when a loaded shotgun next to a bed would be just as convenient as a handgun.
This absurd idea that a shotgun is the “one size fits all” solution
Who the hell is making that assertion? The lady in question seems to be incapable of competently shooting a .38 revolver. I would suggest she try a small 20 gauge shotgun which a petite 60ish female should have little trouble handling with some training/practice.
PS Squeezing the trigger is much more effective than "pulling" it.