My LSD Has a SRO (local cop) on the Jr./Sr. high campus. As far as I know, there are no cops at the elementary schools. While the cop at the secondary campus is there, relates to the kids and is a nice guy, he covers 5 buildings, 2 of which are two story buildings.
The glass doors are locked except during class change times and the main door by the office is not locked. It is guarded by a secretary, who is nice, but I doubt she is trained in any security measures and she is not armed. She is a nice gal, but ineffective from a security standpoint.
So we have a cop who has more territory than he can hope to effectively cover and a secretary who can stop only compliant people. The only substantial benefit to the cop is that he can respond faster than if he were on patrol elsewhere. That is a big advantage, but given the layout of the campus, a determined attacker would not have much trouble causing mayhem. Now, if many teachers were trained and armed, that mayhem would be vastly reduced because they are already there, where the bad action would be. The cop is on campus, but the teachers are at the tip if the spear. I say lets give them an effective spear to use.