It doesn't take any time at all to throw a sling over your shoulder, and even if time is really that critical then the gun will still fire without being slung. It's not like the trigger goes dead until the sling is activated (although that sounds like the kind of asinine "safety feature" the ATF might like to mandate someday, makes about as much sense as magazine safeties anyways).
[Edited] You make a valid point that the carbine can be used without slinging it. but, with respect, it does take more time to throw a sling on. It might not take enough time for you to think it is an issue, but it is not as fast as just grabbing a pistol off a night stand.
You can try it. Get a shot timer. At the buzzer, grab a pistol off of a stand and engage a target.
Next, at the buzzer, grab a carbine leaning against the stand, sling it, and engage a target.
If you want to get fancy, you can try other variations of the same thing.
One handed shooting from low ready (or wherever) and compare it to carbine or shotgun.
Or at the buzzer, grab the weapon of choice, move to a position and engage a target. this will give you time to sling while moving to a position.
You and I agree that bringing as much gun to the threat is a good idea, and carbines/shotguns offer a lot of strengths that pistols do not bring to the table (accuracy, power, speed of target acquisition (with two hands), etc).
I am just not going to knock anybody for choosing a pistol over a carbine/shotgun for speed/maneuverability reasons.
Its a personal choice and they both work. They both have strengths and drawbacks.
How they are measured is up to the user. Speed may be the most important thing to the person. That's fine.
I know that for a few years I did not have a carbine by the bed because I only ever practiced with a pistol. It was a weapon I knew inside and out. I wasn't as confident with my carbine shooting.