Why would you need to renounce US citizenship, and why would you pay double income tax? The US has a tax treaty with New Zealand[1] to minimize (but not eliminate) these types of double-taxation issues.
That's not how it works. If you moved to NZ (or any other country with a US tax treaty) you would basically pay an amount equal to the greater of the two tax bills.
You should do more research if this is an option you're seriously considering.
It's always interesting when I hear US citizens whinge about paying more tax. Heaven forbid you get a functioning healthcare system and a government that actually governs
I was under the apparently mistaken impression that NZ was one of the countries where I would have to pay US tax and NZ tax. I'm no opposed to paying more tax for sane healthcare or functional government. But paying two countries taxes would be prohibitive, and NZ is not exactly cheap.