Because if large-scale nuclear or biological war is reasonable likely then climate change really doesn't matter anyway. End of the world scenarios are always an easy "sell" but they are usually not helpful for constructive progress.
Before nuclear war, lots of constructive things like geoengineering could happen.
You're looking at it from the wrong end. Nuclear war seems unlikely now, but it might become reasonable once half of the world's population is banging on the borders of the other half.
Do you think if e.g. India or Pakistan start experiencing lethal wet-bulb temperatures and people there decide to mass-migrate to survivable lands, only to be stopped at the border and denied entry, will those people and these countries just throw their hands up in the air, seeing there's nothing they could do, and accept imminent death? Or maybe they'll try to threaten or force to be let in, using any means available, up to and including nuclear weapons?
(This applies to all nuclear-armed countries - I mentioned these two, because AFAIK they'll be the first nuclear powers likely to experience lethal wet-bulb temperatures - but that's not the only way climate change could make a country mass-evacuate, and such other factors could hit other nuclear powers first.)
So they commit suicide to escape deadly temperatures? If they nuke the countries they want to move to - how does that play out? The choices of providing local cooling, putting more sulfur dioxide into the atmosphere, shades in space etc. will all look more attractive than extended suicide. That also includes negotiating solutions.
New Zealand is always the obvious "lifeboat". It's a long way from populated area so difficult to get there, and it's fairly easy to sink any ships that try. It's in the southern hemisphere so will be protected from the majority of nuclear war which would be in the northern hemisphere.
Unless someone with nukes decides to threaten NZ to open up the borders for their people, or else.
With global changes this big, we can't expect the usual MAD Mexican Standoff a couple big powers to keep everyone safe. It may be that all nuclear powers (or all that remained after a brief nuclear war) will decide together to politely ask NZ to open up or else.
I say the people threatening with nukes here would turn to more subtle methods of invasion, that's their objectives. They won't destroy it because they can't have it. That'd be a waste of nukes.
Now is there someone threatening another country with nukes at the moment but not using them because he knows that'd be useless anyway and would it prove my point ?
There might not be any. Migration pressure from uninhabitable areas will keep mounting, and some of the countries in the "danger zone" have nukes.