Perhaps, but the common wisdom is to buy the "cheapest house in the best neighborhood", or "its who you know, not what you know" or "you are the friends you keep".
Maybe those aren't true, maybe they're true up to a certain point, but in my experience, people will stretch their budget to put their kids in the better schools, and the rat race starts there. This might not be an issue if you're already a dual professional household earning $200k+ or something where you're deciding between $600k vs $1M houses, but more for whether or not a $80k income family should stretch and buy a $400k house or stick to a $300k house.
(numbers aren't accurate, just trying to show that there exists a tier of society that does have to make those tough choices between living comfortably within their means and offering their kids a meaningfully higher probability of future advancement).
I used to meet people in the NYC area who commuted 1+ hour each way everyday to work 8AM to 6PM at least, they were all doing it so their kids go to the best school district they could afford. I felt sad for them since it basically meant very little time with the kids during the weekdays, no gym, no visiting friends/family, cooking, but they all did it.