The average home price in New Zealand is nearly $1 million. Let’s say that $500k of that is land.
So you are proposing to increase average taxes by $5000, and you appear to talk about that as though that is some trivial amount the average New Zealander can afford. A land tax as you propose is an absolutely massive taxation increase.
Say that a land tax takes 50% of all rental income (a large amount) in New Zealand and puts that into the government - how can you believe that is equitable for renters or owners?
The point of a land tax is to take the land profits from private owners, and put it into government coffers. Note that it doesn’t change the amount that renters pay. You think that it would correct rent prices in New Zealand?
$1 million of land is not extreme wealth - it is only 2 or 3 times an average home. Where do you live that $10000 after tax is not a huge amount of money annually?
Edit: I mean, people talk about land tax as though:
1: empty land is abundant and a problem that needs fixing. Ummmm, empty valuable land is rare because there is already a massive holding cost - either a mortgage or the opportunity cost of what you could invest the money in, if you sold. The point of a land tax is to penalise the owner, but owners are already very significantly penalised!
2: a LVT will fix the problem that developers are just sitting on properties without densification. That is a NIMBY problem, or a zoning problem.
LVT doesn’t fix 1 or 2 above. QED.