Recently it doesn't seem to be playing out as such. The current best LLMs I find marvelously impressive (despite their flaws), and yet... where are all the awesome robots? Why can't I buy a robot that loads my dishwasher for me?
Last year this really started to bug me, and after digging into it with some friends I think we collectively realized something that may be a hint at the answer.
As far as we know, it took roughly 100M-1B years to evolve human level "embodiment" (evolve from single celled organisms to human), but it only took around ~100k-1M for humanity to evolve language, knowledge transfer and abstract reasoning.
So it makes me wonder, is embodiment (advanced robotics) 1000x harder than LLMs from an information processing perspective?