Quite frequently we've had problems with kids, etc being on school property for no other purpose but to commit acts of vandalism and damage. The administrator shot it down, thinking the sign was too threating.
Signage is an important part of school safety and security efforts.
The situation you describe highlights different philosophies about this issue. There are many schools that put up signs that are similar to what you offered. Violators will face federal and state prosecution. The difference in philosophy may stem from an approach which attempts to be inviting rather than punitive. Some schools are using signs that are more positive.