The argument against police in schools does have merit. Mass murderers are a rarity, and most of the time the police officers on school patrol would not be doing anything in support of their primary purpose for being there. The taxpayers would, nonetheless, be burdened with the costs of paying those officers through their taxes.
Also, cops with time on their hands usually find ways of making jackasses out of themselves. They might seek to "justify" their roles by becoming officiously picky-picky, throwing their official weight around.
A much better plan: arm the teachers. Teachers are already trained to teach, tend, and otherwise deal with children and teenagers. And no extra tax money will be needed.