Fragmenting isn't everything, but where rifle rounds are concerned, is a nice benefit.
But depending on the barrel length and bullet choice, it would be incorrect to think a short barrel would be incapable of fragmenting a bullet under no terms. That's just incorrect.
Though, that's why a lot of folks prefer the heavy .223/5.56 rounds so they'll begin to tumble within a couple of inches below impact and cause pretty impressive damage and wound channel, even though the bullet may not fragment
as much due to the lower velocity of the round. In a short barrel, as far as rounds are concerned, heavier is better in my opinion.
Myself, I like to use 75 gr out of my 8-1/2 inch AR upper.
I have one other thought about Short barrels that may meet your criteria that hadn't crossed my mind when I first read your post and replied and I apologize for not thinking about it sooner.
Pistol calibers
let's see, there is 9x19, .45 acp, .22LR (all great for using a suppressor). You don't typically have to worry about fragmentation with them either as they're pretty much designed to mushroom instead of self destructing, but if you're using it for defense, I don't think the 22LR would be up to the task.
Many alternate pistol calibers other than 5.56 will provide enough space for complete (or near complete) powder burn and do a fantastic job using the shorter barrels the rounds are designed for.
Pistol caliber SBR's are very effective and worth considering in my humble opinion. Though many folks will bash Olympic Arms products, they've got the pistol caliber uppers down to an art with no lower reciever modifications, though a magblock or modified magazines would be in order when using the pistol upper. When not using a pistol caliber upper, you can use a standard 5.56/223 upper with no modifications.
And considering for a moment a super heavy 77 gr round .223 is about half the weight of the 147 gr 9mm, the 9 will provide better terminal ballistics in comparison out of a short (10 inch barrel) all things considered.