I really like the last sentence. School shootings are pretty rare, so why muck things up with having a gun around at all. You make a very good point. Still, gun free zones do practically guarantee a shooter that there will be zero armed resistance. So it is hard to say if armed school staff would ultimately help enough to outweigh the improbably but inevitable accidents.
I wouldn't mind a teacher being trained as a reserve deputy and then having a locked handgun safe in their room that only they could open. After school the gun could be transferred to a locked carry box and taken off campus, at which point the teacher/deputy could either wear the gun concealed or just keep it in the locked box until they got it home where they would secure it for the night.
In other words, it is possible to have a gun accessible to a trained teacher at a school without a student getting their hands on it. But nobody could guarantee it 100%.