I still like the shotgun as an option in many situations, and have wondered why they are not used as much by officers these days.
One of the things that makes the shotgun more of a "burden" so to speak, is that even though you have a tremendous amount of firepower at your disposal in each and every round fired, you still have to account for, and are resposible for each one of those projectiles.
While shotguns are awesome for close range anti personnel use, that's their problem- they are really only good for close range. A rifle can do pretty much everything a shotgun can do, and do it at longer ranges, without the danger of a buckshot pellet (or the wad at close range) leaving the pattern, missing the target and possibly hitting something that you really don't want to hit. Granted, it may take 2-3 hits with a .223/5.56 duty carbine to equal the effectiveness that 1 round of 00 Buckshot has, but even a moderately trained person with a rifle can double or triple tap a target in the time it takes a moderately trained person to get off 1 rd of full power buckshot, cycle the action and be back on target again. In this day and age of shrinking budgets and less training, recoil of a 12ga shotgun is one of the main issues. Almost no one wants to use the shotgun because of the high recoil. A decent .223/5.56 carbine has pretty much no recoil, leading to quicker follow up shots and better control for the average Officer.
Another issue, although I think it's really overblown, is armor penetration. 00 buckshot won't penetrate most soft body armor. Backface deformation of the soft armor is more than likely to disable someone wearing soft armor if hit with full power buckshot, but it won't penetrate. With a rifle, soft armor may as well not even be there.
Yet another issue, again somewhat overblown, is ease/speed of reloading. Although the controls are a little different, a carbine operates like an Officer's handgun. The gun runs dry, you dump the empty mag, put a full one in, run the action and you are ready to go. With the shotgun, you have to reload pretty much 1 cartridge at a time into a magazine tube located on the bottom of the gun. Without some serious practice, it is a time consuming, fumble-prone process, and some fumbles can make the shotgun inoperable. And God help you if you accidentally load in a cartridge backwards (yes, it has happened in training). You're done till you can disassemble the shotgun to remove the cartridge.
Closely related is capacity. Every PD I have ever dealt with uses whatever the standard capacity of whatever the base model shotgun is (4 for Rem, 5 for Mossy). Even if they are using extended magazine tubes, that is still only 6-8 cartridges. With a carbine, you have at least 20 cartridges in the magazine and, more often, 30.
With all the liability issues nowadays in LE, it's all about precision (never mind that most Officers can't shoot for anything and will miss a LOT more than they will hit). Up till the past few years, I LOVED the shotgun and would grab it and a small bag with 10-15 extra cartridges out of the cruiser if we had a really bad call. Now, I'll grab my carbine, every time. I completely understand why shotguns are disappearing or getting repurposed for less lethal only for LE. It makes me sad, because nothing says "Stop!" like hitting someone with a round of full power 00 buckshot, but it is what it is.