I'm not saying that Longuns are inferior to pistols all the time or even in general, I'm saying I don't like the blanket statements. First there is still a lot of misinformation out there about what a shotgun will and will not do. One thing that it will not do is open up it's patern into a wide cone at short range. Actualy it's just as easy to miss with a shotgun as a pistol at short range especialy if the shooting stance gets ackward like around corners, under beds, in closets etc.
Now lets talk use of force matrix, safe to say that you are far more likely to need a use of force far below deadly force than to go in shooting. I'm sure you've heard of the stories of someone with a shotgun turning a wrestling match into a gun fight because they couldn't make the weapon safe. When you walk in on the domestic in progress what options have you lost because you know have a shotgun instead of a pistol you could holster.
In your felony stop, great! use everyone with as much firepower as you can, but what happens when it's not the SRT and you and your partner now have five guys from the SRV on the deck and need to cuff them before they get bold, you gonna walk up with a shotgun to cuff them? Need two hands to manage that beast.
Now my biggest point, firepower is not one shot stops, its how quickly you can take out all the targets. If you have to engage in multiple directions, on multiple targets, some at ackward angles, possibly while injured the shotgun or AR is always slower at close range. Try shooting your pistol course with a shotgun and see how your times are!
And my last point is what works for well trained soldiers and LEO's does not translate to civilians well. Longuns take more training to master, if you hand someone a pistol and send them through a house and say point it where you are headed at all times and bingo they will do it 80% correctly. They will also be able to quickly point it at any direction if a target appears. They will naturaly pull the weapon close to the body if grabbed.
Same exercise with a long gun and the weapon is leading around corners, they can't quickly turn to engage targets, feet get twisted all kinds of strange ways on stairs and weapons retention is a total loss.
Shotguns are still a good choice often, just not every single time, just saying there is a big difference between living on a ranch and living on a houseboat, Marine vs 85lb single mom, etc.