No -- common law ascribes different responsibilities to a school during the school day, in comparison to before arriving or after leaving for the day.

https://en.wikipedia.org/wiki/In_loco_parentis

The logic isn't "kids might die in a crash", it is that "schools are responsible for what happens to kids during the school day". The school administration isn't trying to be altruistic, they're trying to avoid liability for a death.