I think that Carlos Hathcock put it best when he said that you needed a range of different firearms for different missions, kind of like a golfer selecting the proper club from a golf bag.
That's whay our department issues several different rifles to different officers. Our ERT/snipers carry their .308 bolt rifles with them on patrol. We also have 10 USGI M-14s that we got from the government. Another 5 officers have G36s, full auto capable, 5.56mm. Another 5 have AR 15s with optics and cans, in case they have to be fired indoors. The rest of the officers who carry rifles have to provide their own. Each officer goes through a one week basic training course before they are allowed to carry a rifle on patrol that covers, among other things, when it is appropriate to employ a high power rifle, and when it is not.
There are advantages and disadvantages to every firearm for police work, from handguns, to shotguns, to rifles. As someone pointed out earlier, we are not the military, we are the civilian police. But years ago, before we issued rifles, I got to find out what it felt like to be pinned down by a sniper who was armed with a rifle while another officer lay dead a few feet from me. At that time we had only handguns and two shotguns (useless) between us. So we do need rifles, and a good balance of types them so that you can respond to a variety of threats.
Regardless, I would not feel the least bit "under-gunned" to have a pistol caliber carbine for my patrol rifle. As several have quite correctly pointed out, having a carbine that uses interchangeable magazines with the officer's handgun makes very, very, good sense. The whole idea of the patrol carbine is that it is always easier to make a first round hit, and out to longer ranges, with a long gun than it is with a handgun. For the patrol officer having a weapon that could be fired accurately out to 100 yards would be our goal. The key is shot placement. An officer who hits what he is aiming at makes everyone safer.
As an investigator with 20 years of experience I have attended numerous autopsies over the years. Over the last few years most of the gunshot deaths that I've seen have been from "popgun" 9mms. They were all just as dead as the one I saw recently who was shot by a 7.62x39mm. One of the guys that I saw killed with a "popgun" 9mm was riding in the backseat of a large, fullsize car. The popgun round penetrated the steel trunklid, penetrated the front wall of the trunk, went through the seat, into his body, and killed him. Actually two rounds did, side-by-side. When he was lying there on the table for the post mortem exam I don't think he really cared too much about whose book said what about stopping power.
I started reading this thread because I was interested in buying my 13 year old son a semi-auto carbine for plinking. While I find the Hi-Point to be almost unbelievably ugly looking, I had heard that they worked. With 9mm ammo being cheap, and us already owning a couple of these worthless popguns (like the one that I carry on duty), a 9mm Hi-Point sounded good for the kid. Sorry if I rambled on too long. But I wanted to present a little different viewpoint than you were getting from another LEO.
If your pistol caliber carbine is dependable, I'd not hesitate for a moment to use it as a tactical weapon, as long as I kept it's limitations in mind.