The idea is nice, philosophically.
As a I'm a little bit jaded based on what I experience as a matter routine, but I personally would not want to carry OTJ even if I had the ability to. Weapons retention (during situations that are much more likely than a shooting) would be a big concern.
The districts choosing to have rapid access vaults are very concerning. If a district or school was to choose to allow carry, it should be on body....ONLY. A locked box in the presence of some students is like an invitation for them to try... (and based on my experiences, and depending on the locking device, some could probably get in.)