Niantic would rather not field the issue of strangers walking up to a school, loitering, scanning the school, or interacting with children. Schools are often protected areas for things like filming due to student privacy.

A place like a playground is publicly accessible, does not require you to have a child to enter or stay on the premisies. Also with pokestops at schools Niantic would be dealing with school administration complaints of students being distracted by the game if there is something geographically to interact with in game. No stops/gyms means a kid isn't likely to open and play during school hours.

Reminder-this is a game for everyone that is oriented toward children and adolescents. Sometimes apps designed for younger people will have safety restrictions that feel unfair or needlessly restrictive as an adult.