They do require an extensive house. Am expensive house gets you into a top public school that feeds into a top college, and makes you neighbors and friends with rich people who can get you a good job or a wealthy spouse.
Even here, though, there's an easy trade-off. Expensive house in good public school catchment, or cheap house + private school. But, don't do both if you're stretched.
[1] e.g. like much of Europe, let you go where you're accepted, regardless of where you live, and let the public funds follow you