Years ago I went to Mt Lebanon shccol. They had a strict policy against biking - to school, to churches that were near the school, and to the park next to the school (before school.) They felt the traffic from cars bringing kids to school was too dangerous.
They thought I was being sassy when I said the logical thing would be to ban the dangerous cars.
I guessing that from a school administrators point of view the combination of kids in cars, kids doing tricks on bikes, people stealing bikes, and kids vandalizing parked bikes would be disconcerting, at best.
Of course, from my point of view, it would be great if they ensured a safe bike route to aschools and provide safe bike parking spaces. They could do things to discourage unhealthy, polluting auto traffic to schools as well.
It strikes me as unlikely that there will be much movement in this direction, soon.
I suspect a lot of the suburban sentiment that gets expressed as "It's such a hassle to have to drive the kids everywhere." is really "Thank god, my kids can't go anywhere on their own and get into trouble."
Mick