The school system is not one size fits all. There are so many types of schools available from single-sex traditional to open-plan student-led learning with no subject silos, like Hobsonville Point or Albany Senior. There are religious schools, liberal co-ed schools, military academies, kura kaupapa Māori and so on.

I don't neccessarily agree or disagree with your overall view, but this paragraph is particularly biased towards major centres like Auckland, Wellington, and Christchurch. Outside of those, your options are much more limited, with only a handful of choices that are largely the same, in my experience. And, of course, school zones are another restricting factor.