So I'm going to say you mean "every GOOD supervisor" because we both know there are slugs who don't want workers because workers generate complaints and generate paperwork. From my experience, school police actively dissuade police work. I had a school cop watch a hit and run suspect walk off from the crash because they weren't supposed to take enforcement actions. Then that plays into the rest of your post. Cops who want to cop don't pursue SRO positions, and those guys are the ones most likely mentally and physically equipped for active shooter situations.
I have a good friend who was a school cop for a bit...right up until he could get hired by us. He's both a hell of a cop and a hell of a person. I've been sitting with him when former students came up and thanked him for something he did for them 10 years ago. He obviously made a difference. Besides being good with kids, he's a veteran, a former (good) competitive fighter, and a go-getter. He also couldn't wait to get out of the school cop position because he knew his brass didn't want him being any of that except the first part and he wanted to be a cop, not just a social worker with a gun.