Every pandemic in history was brought under control using herd immunity, including prior outbreaks of coronavirus.
The only exception I know of is the eradication of smallpox, but that is a very different disease.
However, the impact it had on the Native American population when the (then benefiting from herd immunity) Europeans brought it to the Americas is a stark example of how well herd immunity works.
Even the best vaccines provide less long term immunity than actually catching the disease.
Therefore, by arguing that herd immunity cannot bring coronavirus under control, you are also arguing there will never be an effective vaccine.
The common meaning of bringing a pandemic under control refers to having active methods to deal with it and limit effects, people affected and certainly people dieing.
It's obvious that if you're an island that is far from the rest of the world by a few hours by plane that it's easier to isolate. And that's doubly true for New Zealand.
Oz better hope that that a good vaccine emerges: otherwise they're not going to like "round one" of Covid, much less "round two" which many countries are going through now. Ozzies have no immunity unlike the rest of the world.