is there any useful purpose for one of these things as a semi-auto weapon? ... I just don't see them doing anything a 16" AR can't do.
Pistol caliber carbines goes back a long way. The Winchester rifle was commonly available in pistol rounds such as .32 WCF (Winchester Center Fire), which shared the same case with the .32-20 pistol cartridge, .38-40, etc. It was quite common to have the pistol in your holster and rifle in your saddle scabbard to share the same cal. My grandfather did exactly that... we still have his 1873 Win lever action in the family.
One advantage was that the same ammo could be used in both. When used in a rifle, more velocity and range was obtained.
Also, defensively, there is that range, 20-100 yds, where a rifle is needed over a handgun, even if only a pistol caliber. It is a range where more shots are likely to be fired, at a faster rate, as compared to longer ranges where a true rifle cal would be better. A light recoiling pistol cal is an advantage over a pistol.
I don't think there is anything a pistol cal carbine can do that an AR-15 carbine can't.
As far as wall penetration, go see the "Box o' Truth" series.
A .45ACP carbine that takes 1911 mags, or a 9mm Para carbine that takes your pistols mags could be very handy!