Gavra,
You said,
“One Caveat: The antics needed to get your child into a school is reason enough for someone to want to go OTD (I don’t know if that is Al Pi Halacha or not).”
It is Al Pi Halacha. Schools are mechuyiv to make sure that the precious neshamalach in their care are protected from bad influences. Of course your arn’t supposed to say that Publicly. Actually in public you are supposed to print classified ads in the Yated sating that your school dosn’t discriminate in order to receive Government funds. (you can see those ads evrey week in the yated).
And if a B”D or Rav paskens that the children are a negative influence because the parents didn’t listen to something they said then they are a bad influence and the schools should not and cannot accept them.
There is a slight issue that using the threat of harming the wellfare of little kids in order to blackmail their parents into going along with what you think they should do seems morally repungnant to some…But hey that’s why you gotta keep quiet about it in public!!