I'm not going to enter into the debate of legality, infringement of rights, intimitdation of students (sheeesh), or "Superman Effect" of the helmet.
I was bike riding the Natchez Trace in Mississippi on a perfect all day many years ago. Trucks aren't allowed and the speed limit is 45 MPH. I screwed up and went down HARD. One of those, ankle, knee, hip, shoulder, head type falls. An old first generation hardshell Bell at least saved me a trip to the hospital.
In skiing I was coming onto a near flat slow enough that I decided to skate a bit. There was a couple standing still next to a bridge, I caught an edge, went down and just took the gentleman OUT. He heard me yell, but didn't have time to react. He took the full impact on the back of his helmeted head. It rang his bell, but nothing more.
I was literally knocked out of my bindings by an uphill boarder on a blue run. I landed on my shoulder and head. I was certainly shaken up, but we didn't need to call ski patrol.
None of the above happened while riding or skiing fast, none were in less than perfect weather and on a green and single blue slope. Most importantly, all were "out of nowhere".
I don't believe any of these would have put me or the other person in a box, but I do feel that some professional care would have been necessary.
Guess a helmets kinda like a seatbelt, if you don't have it on you won't have time to put it on when you need it.
All of this is simple antecdotal stuff to you, but to me it's life experience. I always put it on before I walk out the door. Plus, it keeps my old bald head warm.
Five days and counting.