If they had no security cameras, they couldn't. There is no "should" if there's no way of doing something. (Saying I should have stopped Harvey from making landfall makes no sense, for example, if it's not something I could ever do.)
However, schools I've been in have security cameras. If you have the software on your laptop, you can flip from camera to camera and see what's happening. That's real time. It's also recorded.
Every school I've seen in Texas over 1000 students large has had walkie-talkies issued to their admins. All admins. And the cops or security. They can talk back and forth.
"This is #3 to cop2, suspect cited in C hallway heading towards D hall ... turning left into D, past D25, heading to stairs to go to second floor."
I've watched admins track kids on recorded footage as they retraced the kids' steps, watched them as they tracked a suspicious person going down the hall and moving from camera to camera--exactly what they should have done, if they had security cameras in the halls, with the killer. Now, presence of mind is difficult. That's why you drill for these things, train for them, practice them. Coming up with novel approaches under extreme stress is usually not possible. But if you decide what you're going to do and practice it, there's a decent chance that what you do will be at least close to your training. And if it diverges, it might be because given the raw material from training even under stress you still have enough cog capacity to innovate and find better ways or more specific ways to use your skill set. I don't judge administrators or anybody else who acts incorrectly under extreme stress, *unless* it's something they did or really should have trained for.
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