You can't know that. Just like that cop froze up what makes you so sure the teacher is suddenly going to turn into John Rambo. And that he has the presence of mind to set traps for this guy or guys in the midst of that kayos, let alone not cause more of a problem than already exists. Most teachers are Liberals in Coral Springs Florida, and hate guns, You could see that if you watched the TV special the other night ,your plan may work in another state but not in Coral Springs. Most of the parents in that particular school are anti-gun. Just like the teachers. The teachers and coach were indeed heroes but not Gunfighters. I sincerely doubt that 10% of those kids parents own a firearm, I know my son in law doesn't and won't allow them in the house. When I asked him if he wanted me to leave him any of my guns, when the time came, he said he would not touch them. Let's assume that most of those kids parents are the same, don't you think that the teachers in that type of area feel the same way?
Freeze up? It can happen to anyone. PO, contractor, pick any category you like.
In this case the guy basically threw himself at the badguy knowing he was very likely to take bullets. Does that sound someone who would freeze up if he had been armed?
You reap what you sow. If none of these folk want to arm themselves, the police are going to wait outside til it's over, and you don't want to hire private professionals, well, be prepared to possibly see some of your kids in the morgue some day.
And as an afterthought on your earlier comments about paid people to protect being more reliable than teachers I would say, I'm not so sure.
Sure there are some teachers who should not be teachers, some who are good well intended who like it but that's it, and some who see these kids almost as their own. Our charging would be hero sounds like one of the latter to me.
I work as a private contractor now, and my observation is that the experience requirements for many in this business are too low for this kind of task, and taking risks to protect someone else's kids would not be high on many of their list of priorities as individuals. Exceptions yes, in general no.
Peace officers have in general good intentions in the latter regard, but at a school level are not fielded in sufficient numbers on site to deal with this kind of thing head on, on demand. One reason could be demands of other policing in the area, and the other is likely funding - they're expensive.
A volunteer program of vets and ex cops might be the best route. There are private organizations like Oath Keepers that do this for private institutions and businesses, etc already.
Bottom line is, allow teachers to be armed if they please, choose one of these other options, or just keep your kids sitting rabbits for slaughter when they're at school.