1. You assume that it's easy to become a citizen of another country just because you want to. They aren't handed out like candy you know. There are usually set criteria, and these may not be possible to meet.
2. Gaining NZ citizenship wouldn't affect the US citizenship, which would still exist. Renunciation of US citizenship is expensive and the IRS will STILL require you to file for up to 7 years after doing so.
3. The $90k threshold doesn't apply to all income types. Furthermore, in many countries, retirement funds pay out in a lump sum at a certain age. So you might hit 65, retire, and have a $1,000,000 income for the year. The host country doesn't tax that money, because it's already been taxed at the time it was paid IN to the account, earlier in life. The IRS doesn't give a shit about that though - it sees $1M income, it sees you didn't pay taxes to the foreign government on that income (so, no tax credit/deduction is available) and taxes you at the full marginal rate on that income (which has actually already been taxed - double taxation ahoy!) Great to see your retirement nest egg that you have to live on for the rest of your life reduced by 35% or whatever in a single hit.
It's incredibly complex, because every country's local taxation laws are different and the IRS definitions for things seem to assume all countries work the same way as the US. But it all stems from the basic fact that America, alone, taxes non-resident citizens on their world wide income. No other place does that. If they acted like every other country, none of the above would be an issue at all.