Eh, they don't care precisely because they believe they have the privilege to shield themselves, and their descendants from environmental catastrophe. Luxurious fallout bulkers are built right now to do just that: protect themselves and their children from iminent threats, be it mob riots or tsunami or nuclear fallout. They don't give a shit about the rest of us, and why would they? What do they have to gain from caring about us, it's just not in their interest to do that when they could afford to survive through this and we don't. They've already won the logic of the free market in a bloodthirsty, capital-centric world then surely they earned their superiority, and their place as the true, deserving heirs of the Earth reborn. Looking through their eyes, it's just natural selection.
Rich people are never going to limit themselves. Being rich means the freedom to do whatever you want. Rich enough and you can ignore pretty much all laws.
Billionaires are not leaders. They are takers. They must be forced via the law, otherwise they will do nothing besides further enrich themselves beyond their already obscene levels of wealth.
Billionaires somehow embody both the worst behaviors of toddlers and the worst behaviors of most adults, without having any of the redeeming qualities of either.