A double has significant scare factor. Two gaping muzzles put the point across a hair better than a single muzzle.
The pump action has an advantage in making a seriously scary sound when chambering a round, but that sound can also give away your position prematurely.
If kept empty loading two rounds directly into the chambers of a double is faster than loading two rounds into a tube magazine then racking the slide.
Since the brother of a aquaintance got his jaw blown off by a shotgun left loaded behind a door, the gun getting knocked over, I don't keep a scatter gun loaded.
Best to keep a scattergun out where you can grab it fast and shells nearby but not where a kid could find or reach them.
Pistols can be concealed in a drawer, but a shotgun or rifle has to be in the open or in a safe or closet where its not as easy to get to in a hurry.
Aside from this theres the historical reliability of the hammer double with double triggers. Its like having two complete firearms in the same stock. Chances of something disabling both locks is remote, and you could even split a barrel and still have a useable gun.
Academic to me, only shotgun I own is a bolt action Maverick. It stays in its case.