The absolute number of people needed by NZ to offset both brain drain and low native fertility is teeny by global standards.
As such the “tap” can be just barely cracked open and the pressure to immigrate to there from [wherever / everywhere] will be sufficient to provide more applicants than openings.
At least it total. The problem comes when you need fresh college grads and eldercare-givers and instead you get retirees and non-English speaking fruit pickers applying.
Well since the focus of concern is the brain drain, yeah. Do they come in just by opening the tap? Knowing the same things those leaving know, that pay us less there than elsewhere, including Australia? Some might. Less motivated by income and more concerned about their county’s slide to autocracy? Where could those people come from?
I imagine NZ could get all the age 50+ Americans of whatever middle+ income occupation you care to name if they made the immigration process simple and cheap enough.
I was about 50 when I was looking seriously into emigrating there. I was far enough along in my career and in my retirement asset accumulation that I could afford to go there, earn less than US wages in my final career years, and still retire well enough. And plan to retire there. That’s no longer my situation; I’m too old to be willingly going back to work.
But if I was 50 now, and watching my country and my portfolio cratering, I might figure that less wages in NZ with investments there & elsewhere non-US would have me both wealthier and free-er at age 65 than sticking it out while underemployed or unemployed in Depression-era fascist trumpland.
Now as a retirement aged dude with rapidly fading skills, I can boost their headcount and the consumption / investment side of their economy. If they want that and can offer me a way in. But I can’t really help them on the labor side.
One can argue, as you implicitly already did, that for any/everything NZ can offer, Australia can offer a better economic deal and to many more people. True. But the nature of the two cultures and the two topographies are rather different. Such that IMO each would appeal to a mostly disjoint set of Americans.