Let's get something very clear
1. Had New Zealand cut emissions like the Green Party/Alliance since 1990, or any other climate change activists wanted, it would have made zero impact on whether or not the cyclone would have happened. Even accepting that NZ makes a contribution, that contribution is 0.17% of global emissions, according to the Ministry of the Environment. If that were zero, it would have made no difference to the cyclone.
2. Had New Zealand cut emissions like activists wanted, along with all of their other policies, New Zealand would have been measurably poorer with less investment, lower GDP, lower population and less tax revenue for government. New Zealand would have had fewer exports, fewer imports and had even less resilient infrastructure, because the hard left would have ensured all infrastructure was underpriced (so having less money for capital) and there would have been no private investment in most infrastructure.
and if New Zealand DOES slash emissions regardless of cost following this, the odds that another cyclone will devastate part of New Zealand do not change one iota.
Sure, I believe climate change is real and human beings contribute towards it, and efficient reductions in emissions are wise. Yet the best way to respond to the threat of climate change and the threat of natural disasters is wealth, economic growth and building infrastructure for resilience.
Whether it be back-up power for cellsites, bridges that can withstand the debris from cut forests, stopbanks or simply re-emphasising what people can do THEMSELVES for civil defence (non-perishable food, water, batteries for transistor radios).
Shutting down industries, denying people mobility they wish to pay for and kneecapping New Zealand exporters that face competition from subsidised and protected rivals in other countries makes people poorer, it makes it more difficult to pay for more resilience in road, water, communications and energy networks, which ultimately users will (and should) pay for.
It's why Japan survives big earthquakes better than Turkey.