I have British citizenship because my father (my parents) were born in Britain. So I am automatically a British citizen. I assume NZ is similar. Naturally, since I was not born there, the rules don’t apply if I have offspring. Unless they are born there, they don’t get to be citizens. (actually “subjects”).
Most countries in some way acknowledge the children of their citizen as also citizens. Some countries, you will lose your citizenship if you naturalize in another country, some you don’t. There used to be stories in the news about places like Greece, where kids born there and left at age 1 or 2 go back for a visit and are immediately sent to do their basic training and mandatory armed service. Also, kids in Canada born in the USA when there was the Vietnam War draft - go south for a visit, get charged and arrested at the border.
The only bothersome thing is that Canada asks what other countries you are citizens of, on its passort declaration. Technically a passport is property of the country issuing, and Canada cannot for example demand your British passport to prevent you from travelling - but they know about it.
Having British citizenship means I can work anywhere in the EU, not a perk to sneeze at if you are adventurous. I can also bypass most immigration/customs lines going into the EU; but since my wife can’t, I usually use by Canadian passport and take the foreigners line.
As far as taxes - in Canada, for example, and many other countries - you do not have to pay taxes if you do not live there. What consitutes residency - that’s where the details become picky - how long you spend each year, do you own property, have assets, does it look like you’re coming back or have you “severed all ties”? Keeping an RRSP alive (Canadian equivalent of 401K or IRA) is for example, proof that you have not severed ties or may intend to come back. Otehrwise, you pay taxes the last year when you leave, and that’s it until the year you return.
Many complaints in Canada when Israel invaded Lebanon a few years ago. Large numbers of Lebanese had come over and gotten Canadian citizenship, then after several years when the civil war ended, went back home. Suddenly there’s new chaos, and people who had been gone from Canada for a decade or more demanded that “their country” come and get them out; since western countries had the clout to get their people out of the war zone safely. Canada spent millions to evacuate what were essentially regular lebanese citizens.
So I can’t see where it hurts to be a dual citizen.