@RPRNY - I would not confine the issue of "accuracy" to just LEO's. Most civilian CCW's don't exactly have high hit to shots fired ratios either. The vast majority of police shootings are snap judgement, reactionary shootings involving handguns. This is an entirely different stress mechanic than an active shooter engagement and it changes the body far more rapidly and uncontrollably.
I understand your fear, but there are more than a few things to consider here. First, rifles are "more accurate" than handguns are. The longer sight radius, the larger sights, the use of red dots (occasionally) and other aiming devices make the rifle a far better tool for this job than you seem comfortable to admit. Size and weight also helps mitigate recoil and improves follow up shot accuracy tremendously.
Second, the ranges inside of the most common schools is outside that of a handgun. This allows responding personnel to engage threats at much longer distances than with a handgun AND with more accuracy.
Third, The stresses are entirely different and far easier to control in an active shooter situation than the reactionary shootings most LEO's are involved in. Why do you think hit ratios are up in situations in which officers have the initiative in the fight? Because they can slow down and process what is happening and focus on the fundamentals. Active shooter training for me, both at the academy and with my department focused a lot on building search techniques, just sped up to cover more ground quickly (and employ A LOT of movement to contact drills when there is shooting actively going on). No matter how you play this out, short of the guy leaping out of the classroom you are approaching, you have time to effectively concentrate on what you are doing. That's not to say stress doesn't impact your accuracy, it does, but it is far easier to control than the stress of having someone go from cooperative to assaultive on the street.
As for the choice in tool... a 9mm carbine (what few exist in any reliable function) actually doesn't offer much of anything over a 9mm handgun except longer sight radius and recoil reduction through increased weight. The 9mm round does not gain speed in the longer barrel of a PCC and in some cases loses it. About the only PCC caliber that would gain speed are the hot rounds like the .40S&W, 10mm, 357 sig, etc.
Their effectiveness at the ranges inside of a school are dubious. The schools in the jurisdiction I work have hallways that at their extremes are over 100 yards long. A PCC is really struggling at those ranges to make lethal and accurate hits. An AR15 with a 25m battle zero is pretty much within an inch or two of the point of aim at 100 yards and the round is extremely lethal at that range (and beyond). Also, PCC's and handguns in general will penetrate barriers much easier than the higher velocity poodle popper an AR15 is shooting. The last reason NOT to have PCC's is armor penetration. It's going to take a whole different set of body armor to stop a .223 coming from an AR than a handgun round and while I'd like to think that the majority of these monsters shooting up schools don't wear armor, how many are wearing rifle rated armor? Probably very few.
Also, with the flatness of the trajectory of the .223 in the ranges in which a school typically has, there is a lot less stress in aiming knowing that I can put the sights on target and hit within a very small circle of that point of aim no matter what range the person is at. This really helps remove that added stress of having to manually calculate bullet drop at range for the bullet you are shooting.
EDIT: I don't know about other departments, but mine (a smaller town west of Lincoln), the rifle training and shotgun training ammo allotments is near zero. I get 50 rounds of .45ACP a month for the handgun, assuming we have ammo, but the only time we get to do rifle or shotgun practice is in our once a year qualifications with those firearms. The problem with that is two-fold: Does the city have the money to support officers practicing more with their patrol rifles? -and- Is the administration going to muster up enough courage to ask for that money if it is available? In my case, the last question is the biggest hurdle, the first, not so much.