

It depends on which kind of climate disaster we’re facing. If it’s reversible over the next million years, humanity as a species should be fine. The population would be cut down to just a tiny fraction, and the survivors might have to start from pre-industrial tech level.
If it’s irreversible, and the Earth becomes a Venus like hellscape, the whole planet should be pretty much sterilized. Good luck surviving that.
If I understood it correctly, the main problem it can solve is lack of trust. If the involved parties can’t find a single authority to trust, they can use a blockchain instead.
Finding cases like that is a bit tricky. For example, you trust your ISP, your bank, maybe even your government… to some extent… They’re not your best friend, nor do they have to be. You can still trust them enough to take care of certain jobs. You pay your ISP via bank transfer, and they provide the service you signed up for. As long as there’s just enough trust, the system still works and there’s no need to use a blockchain.
Same goes for banks. Most people trust that the bank isn’t going to run away with your money. As long as that trust exists, there’s no need to use a blockchain.