Public schools in NZ are also forbidden from what NZ calls "zoning" which I think in the US is explicit and mandatory through school districts - e.g. the exact opposite.
Despite that, public schools get some reasonable portion of their funding from the council/city/region/district/etc so a public school in a rich neighborhood generally has more funding. The next biggest source of funding is community/parent groups doing fund raising and what not - school fund raisers are common in NZ - but that again means a school in a richer area ends up having more resources.
The end result is that even in a country where there's negligible private school, schools are explicitly prohibited from restricting enrollment geographically, there's a significant difference in outcomes for rich neighborhood school vs poor.
The kids going to such elite institutions (similar to the British public school program for the posh) probably mostly came out of private high schools that also inflated grades, and if SATs are used, they probably had SAT tutors - so they're going to be used to getting top scores on everything, and will complain mightily if that changes.
I don't really think the point of those schools is to really get a top-notch education, anyway - as with the British system, the point is to network with other children from wealthy elite families, which is a launchpad into the upper circles of government, business and media. The Atlantic spelled it out recently:
The answer lies in the specific nature of Ivy League elitism, which is an aristocracy of networks. Ivy League graduates make up 0.4 percent of the country. They are significantly overrepresented in Fortune 500 C-suites, in the House of Representatives, in the Senate, in academia, and in the media.
https://www.theatlantic.com/ideas/archive/2022/01/ivy-league...
As far as anyone who wants a useful education in technology/science/math/engineering, you really want to go to a research-centric school that's small enough to allow you a chance to work directly with active research groups - even in a menial position. If you want to go onto graduate school, that experience is more valuable than anything else. Grades and GRE scores also matter, and will help with things like paid fellowships, but not nearly as much as hands-on experience with a real research group. Also, always take the harder series - a C grade in an advanced physics course for physics majors will mean more than an A grade in the softer version for non-majors, for example.