These instruments of force are necessary to maintain our society. They must exist and be accessible to all in order to keep us all honest, equal and free. It is up to individual people to see that they are used as little as possible. The legitimate use of firearms is as an equalizer - to protect the weak from the strong. Making gun-free zones in just an invitation to kooks.
Nobody needs to know how many guns are in a school.
Let the criminal element wonder. Let them scratch their head and wonder if a teacher does, or doesn't, or if a principal does or doesn't have a gun. You cannot use a law to regulate the people who don't obey laws. The only thing you can use to regulate the people who don't obey the law is force. We need to use law enforcement, not laws, to regulate people who won't obey the law.