That could be taken as an argument that police intervention in schoolyard violence works.

My point isn't that schools are more violent, but that we're correctly identifying that managing school violence is not part of the teacher role, and simply ignoring it as "boys will be boys" isn't good either.

While violence may not be a part of the teacher role, education certainly is. And that sounds like the kind of social education that is an extension of what family should be providing. I'm wary of sending policemen to school, just the same as I'd be wary of sending policemen to families ("violence is not part of the parent role").

It could, but the time period violent crime has been going down and the period that saw far more cops in schools don't completely overlap.

The "more cops deployed in schools" thing lagged the preference for police intervention and legal charges for school-site crimes that previously might have been handled informally (deploying cops to schools was a response to the fact that the cops were being called to schools more often.)

So if it was the change in disciplinary approach that drove the decrease in violent crime, its quite possible that effect would somewhat precede the increase in police deployments in schools.