Surely these hyper competitive neighborhoods are full of already wealthy people? I hear about people "needing" to spend a ton of money on kids as part of this competitive scene and I just don't get it. If you're that worried about them, why not invest that money into a house (which costs the same as e.g. 4 years at Yale, but you could potentially rent it out until they're old enough, and finance it) for them so that they basically start life on barista-FIRE mode?
It's a good question I would just suggest to you a lot of the behavior around wealth doesn't really make sense if you are just doing that kind of back of the napkin math.
Like all the wealthy workaholics who just don't stop. They've so clearly made it and don't have to work anymore, but they can't even take it easy on themselves never mind their kids.
I suspect there is a lot in the psychology of an overachiever that isn't simply turned off when one hits a financial benchmark or has a child. In the latter case, this often seems to make things worse. A parents duty is to care for their child. Having your kid end up being the wealthiest barista sounds about as good a strategy as thinking someone will have good financial sense after winning the lottery. A fool and his money are easily parted. If you worry about what will happen to your kids after you die, as many parents do, simply passing down a bag of money often doesn't feel like enough, even if to others lacking such a luxury this appears indulgent.
But I agree it's a good question and also perhaps has similar implications for broader questions of public policy, such as state driven income redistribution, etc.
It's also good to remember that you never really know what is going on inside other people's homes. Wealthy neighborhoods have all sorts of wrinkles and disparities, even if on balance they are clearly privileged compared to whatever the national mean is. Perhaps the more opulent the neighborhood the more the scenario you lay out is prevalent. There are plenty of neighborhoods with overachievers who have done well that don't yet represent the sort of people you might say posess "generational wealth", where this sort of thing is basically the whole idea. But then again, it's a matter of perspective. I mean you could also probably live in a cheaper neighborhood and spend less money. Questions of work and wealth have always been tied to questions of morals and power. Top schools aren't just about earning potential. They are about access and prestige. They simply don't attract people who just want to get by.
I mean I've done very well in my life; my wife and I both moved up several classes, but I take ownership of educating my kids. My oldest started kindergarten today, but she's already a couple years ahead, and she's only really in school for social reasons. I don't think school is going to help you to avoid being duped. In fact, if these "elite" educations cost as much as a house, that is the first scam to avoid. Poor first lesson to fall for the upper middle class version of a gucci bag!
Similarly, I plan for my kids to go to university, but for social reasons (it's the best place to find a spouse IMO), and that's exactly because I can see that the rational economic choice in the face of uncertainty is not to buy (or finance!) an expensive credential, but to buy a house and not fall for materialism. Books are free if your goal is to learn. An "elite" university is therefore less important than one with strong social pressures against things like casual relationships.
Right, if you're at the level where you could afford the fanciest credentials, you don't actually need them. Then if you're upper middle class (so you don't have unlimited money, but they don't need the credentials), you need to ask why you'd send your kids to college at all. If you've raised an Ivy-calibre kid, presumably they can self-teach with the infinite resources available, so it's not about education.
So the obvious reason for a decently well off family to send their kids to university is because it is far and away the best way to find the person they will marry. Casual dating squanders that opportunity (and promiscuity is linked to higher divorce rates if they do eventually find someone), and they'll never have that chance again. No different from giving your kid a trust to live on and watching them spend it on drugs and partying.
If you're economically secure, immersion in a culture that normalizes positive values is the most important thing you can buy. In fact from that perspective, the hyper-competitive and ambitious culture (to the detriment of e.g. a fulfilling family life) of the Ivys is likely undesirable.