A pistol caliber carbine is great for 3 gun matches when you want to shoot in a space that doesn't allow shooting steel targets with "real" rifle cartridges. It also lets you practice high volume rifle shooting with a round you can reload easily and cheaply.
It's for recreation. I have one in 9mm and it's lots of fun as range gun. If I'm going to war, I'm grabbing my AR.
They've been around since the mid 1800's in this country. I've owned several and still own a Kel-Tec SUB 2000 in 9mm Glock (that means it utilizes any magazine the Glock 17 will run.
The SUB 2000 is a folding "carbine" and makes a great emergency gun to have in your vehicle, a briefcase, or a carry pouch that will hold it. They are actually pretty accurate. Basic stuff that just works.
Ruger used to make a .40S&W rifle which was model PC4. I had one of those and it was very accurate and a great little rifle to own and have at your ready.
OP, I would say so that if someone were a big fan of the .40 S&W, and had one as their carry pistol of choice, the carbine would be a natural choice. As for hunting? Why? The 10mm Auto round would be a much better choice in a hunting carbine.
Extrapolating from the max muzzle velocities for handgun loads, the .40 S&W ought to be a fairly close equivalent to the .357 magnum in a rifle. For 180 gr, maybe slows down a little quicker due to lower BC & SD. Just how that translates into effectiveness on game, I dunno.
[The Lee Modern Reloading Manual 2nd Edition lists a Longshot max load for 180gr. XTP that's ~100fps faster than that for the next fastest powder, and that maybe gets to 1500fps out of an 18" barrel. I wonder if the famous Longshot 'BANG' is still present,]