No, they do not, they only cover a portion. As the owner of a New Zealand investment property...
In NZ, ROI on property is targeted to be around 8% [3]. The owner will take that ROI either in capital increase or in rent. [2]
If the property is appreciating, the rents will be allowed to slow down. If the property stops appreciating, then the rents increase to maintain the ROI. The entire market is targeted at 8%, particularly the property management companies.
Changing the property tax rules changes this equation, with a shift to higher rents.
New Zealand is trying everything to remove demand from the housing market. They first brought in new deposit rules (20% min for owner occupier[4], higher for investment properties 35%+[5]), now they've brought in foreign ownership legislation. It might affect the rate of capital increase, but that will only shift the ROI equation towards rental increases.
The government is looking at building more housing (FINALLY), but they are finding that all the regulations (houses with heating and insulation cost more!) means they can't do it for less that 600-650k [1].
[1] https://www.interest.co.nz/property/95345/housing-minister-s...
[2] https://www.interest.co.nz/saving/rental-yield-indicator
[3] https://www.yourinvestmentpropertymag.com.au/expert-advice/l...
[4] https://sorted.org.nz/guides/home-buying/buying-a-first-home...
[5] https://www.rbnz.govt.nz/education/at-a-glance-series/lvr-re...