The issue is not one of trust (although I suspect a lot of parents would not want firearms around their children,,,they trust teachers to educate them etc, not to defend them). It is rather what works. If teachers/administrators, volunteers...whatever have the freedom of movement to do the job effectively, I have no problem.A lot of teachers by the nature of their jobs do not, and I highly doubt you would ever get teachers to agree to have all teachers in a school armed, which is what it would take under your plan.
Ah, concealed carry. Who would know who has what?