“Also, screening students entering a school building would have stopped this killer.”
Agreed on the security guards - having them armed, and more than one may have helped limit the damage. Maybe, depending on where they were at the time.
Screening wouldn’t have helped. The first shots were fired from the outside through a window - and killed the teacher first. I don’t know if he just went in through the door or the broken windows.
While their may be some collateral damage with armed students or teachers in the classroom - it probably still would have been less dead.
The other thinking is that knowing their are (or could be) armed people at the school would help prevent many of these nutcases from going there in the first place.
So arming the teacher would have proved worthless.