If Rabbi Rechnitz got his kids into a school where every other kid was a child of a person in klei kodesh, how do you think they would feel about themselves after 12 years of school? They wouldn’t feel good about their family or proud of their father as a person. Sure, they’d feel good and take advantage of their position due to his money, but their values wouldn’t be “look up to man who supports community of Torah” but rather “look up to people who work full time/are in chinuch/ in klei kodesh”.
‘In town’, kids tend to be more influenced by the community, as they’re not getting the regular “we do this, they do that” message that OOT’ers naturally send their kids. So it’s more important to send your kid to a school where their peers are on the page you want them to be. OOT there’s one school and everyone goes and the kids turn out fine and tend to have values similar to their parents’.
Not only that, ‘in town’ parents are motivated to send their kid to the “best” school they can get into, hoping their kids will be influenced by the peer pressure and turn into better kids. This doesn’t actually work in practice, as sending your kid to a school where they don’t belong nearly always backfires, but it doesn’t stop people from trying to do what they think is best for their child.
My point is, it’s not all elitism. Some of it is just the natural result of the existence of a spectrum of schools and parents who want x and y for their kids. And that spectrum exists anywhere there is a large enough community to support it.
I don’t know anyone who couldn’t get into any in town school. I know many people who had to push to get into the school of their choice, and others who refused to go to the schools that would accept their kids as a matter of pride. Or who wouldn’t admit that their kid just didn’t fit in the mold of a particular school that all their other kids went to.
There is definitely a problem, but I think it’s more like 5% elitism and 95% situational, rather than vice versa.
If there is also a space problem in Lakewood, that compounds it, but I’ve never heard of anyone who put in the requisite effort and made all the calls and couldn’t get their kid in anywhere.