Or does it just seem that way because students who are serious about studying in the US choose top high schools due to the reputations of those schools in US admissions and/or because people who can afford to attend top NZ high schools are more likely to be capable of funding their education in the US?
No problem. You’ve still got every chance. Studying at a less reputable school means that it’s easier for you to stand out amongst your peers (top universities value you being the #1 student within your school) and they appreciate the unique background you have.
The biggest disadvantage I see is that at a lesser school you’re not likely to perform as well - less competition and academic resources (scholarship training, higher level classes, teacher experience teaching a high level). To get accepted into a school, you’re still going to have to reach/be in the vicinity of their absolute standard. This means if you’re at a school where the second best student is getting a merit endorsement in level 3, you’re still going to have to motivate yourself and find a way to be in the region of a premier scholarship award if you want to get into Harvard.
I was accepted to Harvard and Stanford and won the Robertson from Lindisfarne College in Hawkes Bay, a school that’d only had two people study in the states in our history (and they went to play soccer in Oklahoma or something). Lindisfarne is a great school - we just don’t a history of students applying abroad. Admissions teams definitely hadn’t heard of Lindisfarne before my application, but they were willing to take me despite it being a clear “top school” (that a lot of students come out of). This to show proof that you don’t need to come from a classically top school to get into U.S. universities.
Hope that’s helpful, I’m more than happy to be more specific if you message me directly.