Like I said, you can miss with a shotgun even close up. Go to a shotgun oriented course or match before you opine that they are so much more like to hit. I'd like to see those actual figures.
I like the point of the shotgun hostage shot. Have the shotgun fans tried that with something other than slugs at various distances. It's a touch of a challenge. I've done it in class and matches. You might also note that the wad goes off in various directions and close up will give your loved one quite a whack.
If you only face opponents and no others in the direction of the gun, not a problem. In your house and neighborhood, expanding shot is a problem at distance. If close up, then pattern it - it doesn't fill the room - that's horsepoop.
Another fun nuance is recoil. You may be an expert shotgunner in sports or the range. In extremis, it might not be that much fun. I know a friend who didn't get a good shouldering of the gun making a tight shot around a barricade and dislocated his clavicle. Ouch!
Also, intimidation - TV horsecrap also. Police might face a nut in the street and make a show of force against someone who is acting out. In your house, you don't want to be making a show of it. If you want to challenge the person, you'd better be behind some kind of cover. Standing there and posing - you get shot down. If you are behind cover:
"Yoohoo - I have a shotgun, Go away, you bad man". Silly now. Best to say: I have a gun, the police are called.
A shotgun is a fine weapon to fight with, if you know its pros and cons. It's not a COS play accouterment.
I read a piece where a gun writer says: Well, if you have to use the phone and cover the bad guy, tuck the shotgun under your arm or carry it forward of the trigger guard to balance it.
Critique that plan, class. That does go for other long arms also.
A Brown Bess musket could be used successfully. You could escape in the cloud of smoke, like a ninja.