I know that cavalry like short carbines.
I'm not sure. Some weapons have had one purpose only.
The WW1 Paris Gun could... hit targets as far as Paris. That was it. There was no spotter to make corrections and the stupid thing could fire 20 shots a week.
The German WW2 Jet fighter could fly fast. Alas, turning at high speeds had a 70% chance of jamming its own guns. Turning seems to be a thing fighters might want to do.
The Yamato was a really big battleship. It's often said the problem was airpower. Some analysts have said that even if the age of the battleship was still there and carriers only supported them, the Yamato was still a dud. If it was still the age of battleships, they could have used the resources instead of build 7 kongo class ships, a a crusier, a submarine, and a dozen destroyers. The Yamato DID have a longer gun range than that combination, but I'm suspecting the latter combination would be better.
But all those not-so-practical things had one role they would have been best at. If that single role was a bit more important, then they would shine.
Unfortunately, I can't think of any niche such a carbine would serve. There is such a carbine dated to the late Ashikaga era around 30% the length of a Brown Bess. Tellingly, whenever firearms are mentioned in Japanese warfare at all, they are either longer (for more muzzle velocity probably) or shorter (to be handheld). The use of a saw off carbine I think would be no more useful than a Desert Eagle in WW2, Vietnam War, Somalia (assume ammunition is available as I know it wasn't around WW2)... not any better than anything already available and not having a niche.
But given cavalry like short carbines, wouldn't there be some niche? I can't think of a single use that couldn't be better served off than a pistol though.