The school district my daughter attends prohibits all bikes, scooters, skateboards, mopeds, or anything that can't be registered as a vehicle on their property. Nor are kids up to 5th grade allowed to walk to school alone. But all the schools in her district are nowhere near neighborhoods and there are no sidewalks to connect the communities to the schools. They built all the schools here in rural areas outside of town. It is done as a safety issue and probably as a liability issue. (student accident on school property etc.)
However the school can do nothing if the student here wishes to park his bike off school property I would think. I also figure since his siblings are probably taking the bus, so should this student unless the ride is 2.3 miles, not 23 miles one way. I used to ride my bike a lot to all my schools including elementary but that was in the 70s and early 80s.