I agree that the kids are in danger when left alone and I agree that schools need to develop a policy regarding unsupervised children.
I think the policy would be met with much resistance from parents who come to watch the game and are all too happy to let the younger brother run off some energy playing pick-up football games behind the end zone or over on the practice field, or wherever.
I watched a game a few weeks ago where an administrator confiscated a football from one of the "pick up games" and it wasn't 5 minutes until the irate parent marched over and demanded the ball, gave it back to the kid and blasted the administrator for taking it in the first place...
It's a different world than I grew up in. My dad would have wore me out - and told the administrator to use the ball for a PE class.