Let’s take a look at firearms law (I’m using the NRA’s reference, found here).
Title18, U.S. Code, Title I, Section 921(a)(3)Any Other Weapon (Title II, Sec 5845)
(5) The term "shotgun" means a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder and designed or redesigned and made or remade to use the energy of an explosive to fire through a smooth bore either a number of ball shot or a single projectile for each single pull of the trigger.
(6) The term "short-barreled shotgun" means a shotgun having one or more barrels less than eighteen inches in length and any weapon made from a shotgun (whether by alteration, modification, or otherwise) if such weapon as modified has an overall length of less than twenty-six inches.
(7) The term "rifle" means a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder and designed or redesigned and made or remade to use the energy of an explosive to fire only a single projectile through a rifled bore for each single pull of the trigger.
(8) The term "short-barreled rifle" means a rifle having one or more barrels less than sixteen inches in length and any weapon made from a rifle (whether by alteration, modification, or otherwise) if such weapon, as modified, has an overall length of less than twenty-six inches.
(29) The term "handgun" means--;
(A) a firearm which has a short stock and is designed to be held and fired by the use of a single hand
(e) Any other weapon.:The term "any other weapon" means any weapon or device capable of being concealed on the person from which a shot can be discharged through the energy of an explosive, a pistol or revolver having a barrel with a smooth bore designed or redesigned to fire a fixed shotgun shell, weapons with combination shotgun and rifle barrels 12 inches or more, less than 18 inches in length, from which only a single discharge can be made from either barrel without manual reloading, and shall include any such weapon which may be readily restored to fire.Such term shall not include a pistol or a revolver having a rifled bore, or rifled bores, or weapons designed, made, or intended to be fired from the shoulder and not capable of firing fixed ammunition.A little bit of history – originally, handguns were going to be considered as Any Other Weapon (AOW), and charged a burdensome tax. With that little tidbit, the definitions of Short-Barreled-Rifles (SBR) and Short-Barreled-Shotguns (SBS) becomes clear as well; they are attempts to make sure that handguns cannot be legally created out of rifles and shotguns, at least not without registering them and paying an even more burdensome tax.
The classifications of was changed at the eleventh hour of lawmaking, but the definitions of AOW, SBS, and SBR were left in, and a tight definition of Handgun was added. The BATF has held since then that the attachment of a stock to handgun makes it a rifle (most likely short-barreled, since very few handguns have the necessary 16” barrel) and the attachment of a forward grip makes the combination AOW. In both cases, possession of the stock or grip without a corresponding registered AOE or SBR is considered “constructive possession”. This has been allowed to stand so far because no-one was sure if the Second Amendment guaranteed an individual right to a handgun or not, until the Heller decision. Now, of course, we have the guaranteed right to possess a functional firearm (specifically a handgun) in the home for the purposes of self-defense.
Given that, I can’t see the restrictions on SBS, SBR, or AOW standing. Each in their own way exists to prevent the conversion of a non-handgun into a handgun (or, in the case of AOW, prevents making a handgun more effective). Since we now have a guaranteed right to possess a functional handgun, there’s no reason to restrict someone from having a short-barreled firearm, &c.
I expect the only reason these haven’t been challenged so far is due to lack of bandwidth on the part of the relevant organizations.