Expanding on the bead sight thing for a moment:
Whenever you mention bead sights on the internet, someone will inevitably show up and proclaim that they use a bead just fine. And I'm sure some of them actually have fired a shotgun with defensive munitions in the gun (buckshot, slugs) and can what they intend.
That's cool.
...but that depends on how the gun interacts with your body. The drop on the comb of a shotgun is crucial to wing shooters because that has huge implications for how they mount the gun. At the highest levels, the gun's fit is tailored to their exact physiology by custom gun makers who take fastidious measurement at several points of contact to get the gun to fit. They even have the buyer point a shotgun at their face so they can fine tune the alignment of the gun with the customer's eye when they mount it.
Absolutely none of this is happening on a police issue shotgun. Or, frankly, one people are using for self defense.
I guarantee you that almost nobody else walking this planet has the exact same measurements as I do. Height, build, length of your neck, shape and placement of your cheek bones on the skull, the length of your arms...all that varies from person to person and all of that has relevance to exactly where your eyeball ends up in relation to the bead on a shotgun. That's why it's a fucking terrible sighting system for a defensive shotgun.