Not saying I disagree with you but... historical immigration policy certainly impacts "today's" population size that you're using to draw your comparison.
The US has an incredibly wealthy continent at its disposal, full of mineral wealth and fertile farmland, with centuries of infrastructure, close to global trading hubs.
New Zealand has a couple of mid-sized islands, neither of which are particularly good for agriculture or mineral wealth, are a very long way from trading hubs, and has the shortest history of built infrastructure of all western democracies.
But if you want "historical immigration policy", the US's population has tripled since WWI while NZ's has quadrupled; similar growth with NZ having a bit more.
Your point is reasonable, but you are calculating rates from a vastly different denominator. At some point, I do think that sheer scale has to factor into the analysis.