Are long guns necessary, given the distances involved and the clumsiness of carrying one all day...
Yes. Long guns are consistently more accurate than handguns due to the more stable extended grip surface and longer sight lines. It’s why the soldiers and Marines use long guns when expecting close quarters engagements. The KelTec SUB2000 proposed is a compact foldable pistol caliber sweetie. Perfect for its proposed use.
One can always hit better with a shoulder fired gun than a handgun.
One might reasonably infer that the Sheriff is planning on short barrel AR type weapons...
But not necessarily. A pistol caliber carbine (i.e. 9mm) with an 8 inch barrel would actually be quite handy, but might still be referred to a a “long gun” because it’s shoulder fired.
Or .300 Blackout. Some Israeli teachers are still equipped with M1 carbines.
Honestly one could make a case for a .22 as a defensive weapon with all the kids present.