I think its done this way these days out of a concern for child safety. Especially with elementary age kids, the school needs to know who is picking up the kid. (You often have to have a thing with your kids name and grade hanging from your rearview mirror) They don't want to be responsible for strangers, or an estranged relative kidnapping a child.

They are also concerned about the kids walking through parking lots or the pickup line and getting hit by a car.

Those things happened enough times, and school districts got sued enough times that we end up with what you see above.