The robots will serve the rich elite who survive the climate armageddon, or at least, replace the labor of the bottom of the ladder of economic success. Expect mass famines and a never ending global refugee crisis. They’re building the wall today to have a physical barrier in place before a flood of people seeking places that are still habitable.
Expect massive domestic population declines, and to be told that climate change isn’t a cause of death, it was “natural causes”. Nothing is wrong, but we need more labor. Robots will save us.
Can’t be unemployed if you died domestically for natural causes with nobody to blame, so unemployment rate is mitigated.
ETA I don’t agree with all the thinking here, but I believe that billionaires think very differently than the rest of us, and I find this a very plausible “logic”.