To my understanding, the LAPD's elite SIS detectives use 12ga shotguns with Surefire fore-ends & pistol grips.
You have assumed that the LAPD SIS gets to use what they want or gets to use the "best" gear rather than what a bureaucrat chose or because the bid came in the cheapest. It may be that each and every detective wanted a pistol grip, but it might have nothing whatsoever to do with their choice. I'll bet you we could find many, many more cops with standard stocks - and that, too, wouldn't mean very much.
Pistol grips are a choice, I find them more trouble than they are worth. They tangle in the sling, on a Mossberg they are undeniably useless, and they often travel hand in hand with the equally tacticool and useless adjustable stocks favored by mall ninjas (figure out what LOP you need and buy that stock). In my experience, a pistol grip on a shotgun slows down the mount and cheek weld, and thus the first shot, so I think they are more for "show" than "go." I feel the same way about red dot sights on a shotgun; it's a shotgun, friends, if you can't put rounds on target in shotgun range without a red dot sight, you don't need a red dot sight, you need practice. Don't even get me started on the "just as good as an Aimpoint" red dot sights.....
Worst of all is the vertical fore grip on a pump shotgun. Tell me how that improves anything for anyone. It's just more Tapco crap that someone will buy and stick on their gun without any concept of whether or how it enhances the utility of the gun.
To all the people who just got offended, it's an opinion, nothing more. I like Thai food, the color blue, brunettes, and I hate cauliflower. Don't get bent if you disagree, especially if your pistol grip adjustable stock just as good as an Aimpoint red dot sight vertical fore grip Tapco catalog shotgun works for you.