First, stats show that foreign buyers own ~3% of homes. Everything else is kiwi-owned.
Second, there is another thing going on here -- KiwiBuild. Basically, government funds and builds 'affordable houses'. Prices (in NZD) are $500-650k, but now they want to have even more affordable houses - $300k. For comparison, actual average house price in Auckland is above $1kk.
My wife and I work really hard, NZ is not our country, English is not our language, the culture is different, we have nothing to inherit here. Why should we pay (with our taxes) for poor kiwis who can't afford a house? Shouldn't they work harder instead? Get education, get better job.
We wish we could buy a $1kk+ house in Auckland too, but we can't. If you can't afford a house, then buy an apartment because they are much cheaper. Yes, it is not that fancy, but at least you'll have a place to live in.
I mean, yeah, Labour party is in power in NZ at the moment, hence such policies like 'Let's increase salaries to poor workers, let's give them houses, let's increase maternity leave etc.'. The problem is that somebody has to pay for that.
UPD: another problem in my opinion is that Kiwi culture is very different. NZ is isolated from the rest of the world. It is very quiet here, people are very relaxed, everything goes slow. People are not used to work hard (in my opinion). It is common here to spend a year or two doing nothing, just traveling around the world after graduation. Many people don't want to build a career, they want to 'try many different jobs, find themselves, enjoy life'. Many people live with their parents, start thinking about career at the age of 30-35. At work, if it is 4pm (sometimes 5pm) -- people just leave and go home. "We have an urgent task" here means that it must be done within a week. In schools they teach children that everyone is a winner -- even if you have poor marks. Also, if there are any competitive games/sports, then sometimes they make it that the winner is not the one who actually won, but the one whose turn today is. And so on. Hence many people here, when they grow up, are not used to fight for survival. Just enjoy their quiet life in a beautiful country. But then they are 35, have no money, no career, but want a fancy house...
Sorry if I'm being too harsh, don't mean to offend. But this is my take on Kiwi culture, the way I see it as a non-native.