Any number of armed school personnel could have made this situation WORSE by firing into a wild crowd in an attempt to attack the shooter, whom they might not even identify correctly in the first place.
Keep in mind that school personnel are NOT tasked with protecting children from violent assault threats. They are tasked with education and a kind of child care for 7-8 hours a day. School systems already have tremendous difficult providing support for larger scale issues that fall outside of those realms, and we shouldn't expect that arming school staff would make for anything other than a climate in which those weapons will be used against students. We already have enough problems with making school systems more like prisons, arming the staff is not a solution to fixing that.