Why wouldn't they be dumb?
Most people who use a shot gun for home defense are either smart enough to understand how a bullet or shot penetrates (because a shot gun will go through walls but often not be deadly a few feet away from the wall on the other side where a bullet can go through multiple walls and remain deadly depending on the gun) or they picked it because they have other things to be concerned about besides humans invading. Wild animals and rodents are around a lot of places and just as viable of a concern in home defense as an intruding human might be.
I keep several loaded shotguns around. My favorite, a bolt action savage, I keep one round of 000 buck and two rounds of #8 or #6 shot loaded at all times and I have a stock wrap which 8 more of the same ammo is present if needed. I have coyotes, a certain type of vulture, and rodents like rabbits
(that eat my garden) and groundhogs
(that destroy beans and create holes for the cattle to step in and break a leg) to deal with. The vultures I only have to worry about right after a birth until it is weaned. Black vultures will attack young calves, piglets, chicks, and so on. And yes, I know it is illegal to kill them, but just like speeding, you got to be caught first.
But if you think someone with a shotgun for home defense is stupid, you are going to be really surprised when you meet them. You have either been watching too many movies or hanging out with the wrong people.