Along with your reasoning, my big concern is some thug posing as a student gets the weapon away from the teacher......then, here we go...
If I were a public school teacher and carrying, I would choose to IWB or pocket carry, and concealed would mean what it says. The kids would not know I was carrying. In almost any school, I would also carry empty chamber because of the relative risk of an "oopsie" versus the risk of needing that firearm without even the time to rack the slide. As much as I love Glocks, I certainly would not carry a compact Glock with a round in the chamber for school duty unless I expected to need it more than once a year.
I also suspect teachers feel more attachment toward their students and toward children in general than the school-assigned police officers do, so teachers would be more likely to confront a shooter than the Coward of Broward, Camera Hogg, and their ilk. So, yes, schools should permit trained and stable teachers to carry responsibly while on school property.
That is a concern.
There should probably be training and procedures on securing the weapon on school premises.
And while that could delay a response a little, it would still be better than what happened last time.