More often than not pistol caliber carbines are purchased so the buyer can pretend he has a submachinegun.
Granted, a 9mm version of the AR can be useful for indoor practice at ranges that cannot or will not accommodate rifles. Otherwise I see little use for something the size of a carbine that shoots pistol ammunition.
I can think of a couple of good uses right off the top of my head.
1: A gun for people who do not have a pistol permit to use at ranges that can't accommodate rifles. I have used my Sub2k for exactly this reason on a number of occasions in the past when my range guest did not have a pistol permit. It's been a useful tool in introducing the inexperienced to the sport for this same reason.
2: It's easier to legally transport a rifle than it is a pistol between state lines. NY state pistol permits have reciprocity with so few states. Most NY permit holders do not have out of state permits, and even if they do permits such as Florida and Utah don't cover all the bases. If someone wants to do some shooting in another state, again at a range where rifle calibers aren't allowed, then a pistol caliber carbine would be the thing to have. Also, what about personal protection while traveling ? I am of course talking about taking whatever legal steps are required during the actual act of traveling itself (I.E. Proper locked case, unloaded, etc), but in many states I think it would at least be legal to possess the carbine rifle in hotel rooms, friends houses, or.. whatever. And something so compact like a folding carbine might be optimal in such a case. I've never actually used mine for travel purposes, and I'm sure legallity of that would vary by state, so that's just a thought.