It should go without saying the ATF tries to ban ammo as an exercise in just banning it - there are millions of AR's with "rifle" barrels shooting it, the pistol population is still pretty slim.
A 10.5" AR does have some significant advantages. That length barrel is the preferred one for shipboarding operations, and there are those who use it for storming things like Pakistani townhouses. For us - it's about a 15% velocity loss, which makes it still effective for self defense.
Even hunting - which is why I'm building one. Sure, I have a 6.8 16" carbine for rifle season, but when pistol season rolls around, I can use the AR 10.5" and it still is effective to 200m or more. Accuracy is up to me, the bullet is still effective. And it's not about shooting one particular military round and then worrying about it's fragmentation velocity. It's about shooting open tip ammo that is known to expand well which delivers sufficient force.
Which also goes to self defense - and most of that is conducted at much closer ranges. If at home or in your yard, things are usually in handgun range, but handgun ammo can be less than optimal in some circumstance.
If it's a pistol, then there are also advantages that a "rifle" cannot enjoy. The use and carry of a pistol is now determined a lot more by CCW laws which allow concealed carry but ready to hand - including the front seat of your vehicle. On the other hand, a rifle is often restricted in many states due to anti-poaching laws which require it be unloaded, cased, and stored in the trunk. Carrying it otherwise would create difficulties in a traffic stop as it raises further questions of illegality.
Pistols can traverse state lines, whether an AR, Glock or 1911 makes no difference. But a SBR - as registered with the ATF - requires advance permission from the Feds beforehand. They offer a one year certificate which has to be renewed.
Of course, all of this is moot if you are found in New Jersey with either of them, but in states where the Pistol is legal and the rifle is restricted, and SBR's even banned, it's an easy choice to make.
An AR pistol is essentially identical to the SBR - the only difference between the two woulc be the stock, which constitutes a flat vertical surface to hold it against the shoulder. Two different interpretations in law, same identical ballistic profile, tho. Except in one regard - accuracy.
A stock reduces the wobble of the rear of the gun and makes sighting easier, enhancing the ability of the shooter as they have less variations and a steadier rest. But - it can't make them more accurate than the gun and their inherent ability. A pistol doesn't have that aim enhancing accessory - but with training the shooter can discipline themselves and become just as good again.
It's not that big an enhancement in accuracy when the purpose of a 10.5" barreled weapon is considered. These are close range weapons, the barrels shortened for maneuverability and handling. Most targets will be less than 100m, which means a good shooter will be putting groups right at the capability of the weapon at 2MOA, or, 2". And the average target, human or deer, has an 18" COM, or 18MOA. For hunting or combat purposes, the gun is still accurate enough.
Is a 10.5" barrel louder, yes, they are pushing another 8-10,000 psi at the muzzle because it's shorter. They are NOT expelling burning powder, tho, it's the unburnt gas hitting more oxygen that creates a fireball. That depends on the load, too, as even the military has gone to a low flash formula in the Mk262 77 gr OTM. As for the noise, muffs are the common answer, and most who shoot competitively use electronic muffs with active shot suppression and amplification, too. For $100 - the street price on Peltor Sport Tacs - you get plenty of protection and enhanced hearing of movement much further away than normal. A short barreled gun isn't a hindrance in that regard - it's a reason to get the muffs and enjoy their advantages. They are issue with the small teams that normally shoot 10.5" barreled guns anyway.
So, there are some good reasons for AR pistols, and they can be a better option than a temporary halfway house to being a government inspected and approved gun owner. For some, that's the icing on the cake, as we don't need no stinkin Stamps allowing us to own a gun.
There's more but it's the end of the evening and a long day ahead.