At a typical middle or high school, most of the electric two-wheelers are not e-bikes; they are more powerful, faster, “cooler” e-motos. E-motos are not street legal for any age.
The number of legal throttle e-bikes is often zero or close to it. It is difficult for untrained school and law enforcement personnel to tell the difference.
For this reason, schools are banning all throttle e-wheels. It is the safest, easiest-to-administer approach.