Ever car in our fleet has a shotgun in a rack. Every patrol officer has a Tazer on their belt. Our bean bag guns are just a standard 870 with an orange stock and special rounds. I check out a bean bag gun at the beginning of every shift. Myself and many officers also have personal ARs in the car.
Our swat team has used the shotgun Tazer rounds in the past. I believe they are sometimes, but not always, effective, much like the handheld variety.
A lot of people think carbines are overkill or are for mass shooting scenarios. I've had several people say "you are a cop, not in the army!" Almost once a month we have some crazy person shooting a handgun in their house or front yard. These people are literally crazy. A lot of them probably don't mean harm, they just don't know what is going on. Your best bet in that situation is find cover and stay at a distance. A carbine allows you to stay 75 yards away, call in someone to negotiate, and still be ready to end the threat if necessary. If someone can get close while still behind cover, the bean bag rounds can effectively end the threat as well, but we never use it without lethal cover set up in case the rounds are ineffective.
All that said, I can't think of a time when I would reach for a standard shotgun.