There's a book by Malcolm Gladwell called Outliers. Notionally it's about how exceptional people go about becoming exceptional but along the way it tells you many times over that social background is by FAR the biggest indicator of future success.
The so-called middle classes (massive umbrella term) invest in their kids by passing on how to study, the value of study, how to talk to superiors without being deferential or chippy, etc, and then sometimes using connections to get them a broader range of experiences early on.
If you are the sort of parent who places value in the above, the last thing you are going to want to do is to send your child to a school where in social terms (peer pressure/lack of investment from teachers, perhaps, I don't know) that work stands a good chance of being undone.
(I write this as someone who received very little concrete help as I grew up, and went to a lazy highland comp where I can only assume the teachers are after a quieter life. I married a public school educated academic. Feel the weight of that chip! Gnnnnghghghg!)