Expensive, impractical, some kids getting bit.
The key question I am posing is "Would a trained dog be EFFECTIVE" at neutralizing a shooter. Are there specific reasons why that wouldn't work? I thought of one, large dogs have problems running on linoleum type floors typical in a school so their speed is effected.
I thought of one, large dogs have problems running on linoleum type floors typical in a school so their speed is effected.
While a dog's speed may be somewhat diminished by the flooring's relative lack of friction, the greater challenge to the dog will be turns and stopping, although the shooter's body, upon the dog's hitting it, will provide enough resistance to adequately mitigate the stopping problem. Unfortunately, a bullet hitting the dog, regardless of whether it hits the bulletproof vest you suggested or hits the dog's unprotected bits -- particularly the bits that one sees when a dog is running straight on toward one -- will also mitigate the stopping problem, regardless of whether it kills the dog.
Even though wearing body armor may prevent a bullet from penetrating one's skin, one is nonetheless affected by the force of the impact, which is akin to being hit by a club. In other words, the impact alone packs quite a wallop, and that's on a human. The resistive force is even more impactful on a less massive creature. So while there's no guarantee that the shooter's bullets will hit the dog, any one that does will stop the dog's advance.
That said, I think your suggestion has some merit and I acknowledge its tactical value: the shooter must address the threat of the approaching dog before proceeding to shoot more humans. In light of that sending in several attack dogs could well be effective in neutralizing the shooter because unless the shooter is proficient in parrying dog attacks, only one needs to get to the shooter. Also, seeing a phalanx of dogs bearing down, a shooter is very likely to disengage his/her assault on humans, perhaps even taking flight/cover from them and not resuming the attack on people.
The biggest shortcoming with your proposal is that it is reactive rather than proactive. There's no shortage of effective tactical responses to an active shooter; the dog idea is but another, and I suspect it's one that law enforcement professionals consider on a situation-by-situation basis. The problem the country faces is not how to take down an active shooter, but rather (1) how to materially reduce a would-be active shooter's means and opportunity to become an active shooter and (2) how to materially dissuade a would-be active shooter from construing to become an active shooter.
Would security guards (professional ones like the Secret Service or other folks who provide protection for folks paying "big coin" for it) accompanied by a pair of dogs (with or without body armor) may have some deterring impact, though I have no way to quantify that impact or to say for sure that it will. After all, active shooters don't think rationally, other than perhaps with regard to planning their attacks.