Annual GDP of a country != the current sum total net worth of its population. Deleting the poorest half of the US population would destroy the annual GDP, which is built on the labor of said population. Theoretically, as the GDP of a nation grows, so does the quality of life of its population through better access to everything money can buy. It kinda doesn't matter how many billionaires there are if the rest of the population is still able to buy air conditioners, health care, sturdier houses, pay taxes, and generally afford the things that make the climate the least of their worries, as there are super diminishing returns on quality of life past a certain income level (all other arguments against billionaires are outside the scope of this comment).

Developed countries are quite well equipped (as in they're rich enough) to be able to adapt to the changing climate as needed. They can buy air conditioners, build dikes, choose not to build houses in areas prone to climate disaster, etc., all if which is insanely cheaper than attempting to reduce global temperature (though that's not an argument against any attempt to reduce global temperature). Making under-developed countries richer allows them to stop doing the "worser" things that aggravate climate change and make their populations unhealthy (like burning wood for a lot of their energy needs).

(This comment is just an elaboration on the arguments in the book I mentioned—not me being an expert.)

As @pseudobry mentions: 'the book uses GDP as a "human welfare" metric'.

I don't think anybody here (even the author of the book presumably) is suggesting that they are cause and effect, but they do appear to be correlated.

Also just because 50% have 1% of the wealth, doesn't mean they don't contribute towards the wealth of the other 50% of people holding 99% of the wealth. For example, your boss gets the majority of the profit, but they couldn't run the company by themselves.