Texas...
The reason some agencies are choosing carbines are various and have little to do with home defense.
Defense would insinuate defending... quite the opposite of an offensive operation (executing a search warrant, for example). If one is hunkered down or slowly and methodically searching in a typical HD situation, it is quite a different scenario than a dynamic entry. Actually, it is EXTREMELY different.
Different weapons for different purposes.
If I'm defending a small space (a room, hallway, etc.), I want a 12 gauge with 00 buckshot (my Colt 1911 on the hip to boot). I can gather my family and while they are evacuating or what have you, I can hold the fort... more or less stationary... until my blue cavalry arrives. The purpose of HD is to defend, to protect your family... not go out searching for the threat; but rather, shielding your loved ones from the threat.
If I'm performing a dynamic entry, then a smaller, easy to handle, lighter carbine is what I'd reach for. Something I can sling quickly to cuff a turd, and at the same time reach out and touch a longer distance threat.
One is better suited for offensive purposes, the other, defensive.
I work for one of the 10 largest LE agencies in the USA... we issue both 12 gauge 870's and carbines.
Of course, this is just opinion. I've participated in countless entries, and the rationale for my statements are based on my training and experiences. To each their own, but I'm certain the top 'gun guys' would agree that the 12 gauge with 00 buck is the way to go for HD.