CGP Grey recently put out a video along very similar lines. Worth 15 mins: https://www.youtube.com/watch?v=7Pq-S557XQU&list=UU2C_jShtL7...
He blatantly ignores the issue of energy constraints, more specifically the concept of embodied energy[0], which in the near future will be a very real very limiting factor that right now goes unnoticed because we're burning up energy reserves the earth has built up for hundreds of millions of years. If we do look at this from an energy spending point of view.. this robot/AI revolution is gonna have a few interesting…
I'm not promoting this; I'm just predicting it. The sustainability of fossil fuels will be reflected in prices. More demand, political restrictions, and fewer new discoveries: prices go up; conservation, carbon sequestration/removal tech, and growing efficiencies supplemented by new sources such as fracked gas: prices relax. At some point (you say "very near", I say no one knows), hydrocarbon prices will go so high that the developed world will either have to voluntarily undevelop (not going to happen politically) or pay what it costs to solve some nuke problems and live with others, and we will continue to grow our use of energy.
The spread of robotics will proceed apace.