Is there another reason the school would be unwilling to put any limitations into a binding agreement?"
The thread for proposals is flawed in that the actual parties are not interested in posting suggestions, assuming that you and Mr Sanctimonious are as independent on the issue as you claim.
The neighbors haven't posted. The school hasn't. As a school supporter, I have, but I can't validate the school's position, as I'm not qualified.
And despite what you say, the school has entered into an agreement with the neighbors, with specific times and days, only to see (other?) neighbors sue. We don't know, because they are also anonymous.
Like you and I, on this board.