I have not personally ever seen an LE organization use an SBR with a barrel length less than 10.x" (meaning no one using "Pistol length barrels"). Not saying someone out there isnt doing but it I have not seen it where I am.
That being said about shorter barrel length and .223/5.56 ballistics sort of a side topic
(btw neither TXPlt or neophyte said this in their above posts so this response is not to them but rather a side note to something they said for other people in general).
I hear a lot in different forums or different places the comments about "how ballistics suck" out of shorter barrels when people start talking about SBRs and pistol length builds and anything less than a 20" musket barrel lol.
First of, yes anything sub 10" (like 7.x" builds are ballistically terrible no matter what in .223/5.56).
However for the 10.x" to 16" guns... you can greatly mitigate the ballistic property loss of your shorter carbine to SBR length guns by just using better ammo. Especially for the guns used for defensive purposes. It's almost the year 2020... and just like the handgun calibers... defensive carbine ammo optimized with powders for shorter barrels and capped with better bullets are out there now people lol. and have been for quite some time actually.
It sort of amuses me when I ask someone what they use to shoot coyotes or other game/pests with and they come at you with all sorts of handy dandy awesome specialty hunting loads but when you ask them what they load into their "home defense" SBR or longer braced pistol or carbine they say 55 grain M193 ball or 62 grain M855 Green tips.
Both of which are well... poor performers. (The military doesn't even use the M855 any more and have moved onto the M855A1 brown tips which are loaded way hotter, higher pressure and has and entirely different bullet design and makeup. (it also significantly wears down bolt and barrel life and requires the newer updated magazine followers to feed right).
Most people dont' carry crappy ball training/practice ammo in their handguns for self defense, nor do they carry that kind of ammo to hunt with... but many do in their "self defense carbine/rifle/SBR/braced pistol".
Why?
Plenty of awesome defensive loads are out there that preform extremely well out of shorter barrels and give you much better ballistics (at range out of shorter barrels), through intermediate barriers and much better for in target results if you actually had to shoot someone in a justifiable defensive situation.
5.56 mm Federal 62 gr Trophy Bonded Bear Claw (TBBC) bonded JSP
Winchester 64 gr solid base bonded JSP
Hornady TAP
Hornady 55 gr GMX
Black Hills 50 gr TSX
Speer 55 gr Gold Dots
Sig 60gr EHHT
etc etc...
Sig also makes a great 120gr .300 blackout super sonic round specifically for sort barreled (sub 9" barreled SBRs or braced pistols.
(optimal barrel length for 300 blackout is a 9" barrel, less than 9 inches in the 8-7.x" range you start to see the same problems as with the 10-12" .223/5.56 barrels
Yes this ammo is a lot more expensive but you really only need to buy enough of it to make sure it functions reliably in your gun and then to figure out any zero differences if you have optics. And then just have a couple mags of it or whatever the same as your defensive handgun. Also cycle it out as needed (Just as with a pistol round I would not recommend repeatedly chambering the same round over and over again with .223/5.56.)
In our agency guns we carry one load for work/duty use and then use the cheaper ball ammo for training purposes. The optics whether they be red dots or low power magnified are zeroed for the good stuff.
The bullets are the same weight and we have found that their is negligible to zero differences between swapping ammo types. We use a "50/200" zero for our carbines/SBRs and typically the amount of change between zeros with duty ammo vs training is none to .25 MOA sometimes an inch. Which translates to each operator just knowing that if they need to make an adjustment they just need to adjust a couple clicks on their optics for training if at all. but the point being... its not a big deal.
Obviously if you are using a defensive round that is significantly different than your training round you will see more variance.
Long story short, if people feed their cabines crap ammo, then they cant really complain about crap ballistic performance when there is stuff out there that will address all those issues in shorter barreled guns that will work fine in any engagement distances one could probably reasonably expect to justify a defensive shoot... and in most cases it will still work a whole lot farther than that too.