Why do you think the poor won't have AGI in their pockets and robots as well? If we look at how LLMs are evolving, they become easier to run on edge, and there are so many of them being pushed out every day. Costs for robotic hardware are also going down fast. Intelligence is free to have, unlike UBI. And robots can build robots, or make it cheaper to build robots.
For example instead of AI, take web search - if you are rich or poor, you get the same search space and tools. The rich are not searching better. They don't have radically better operating systems, social networks or phones. Same thing with content - we all have the same massive pool of content to watch. The rich don't have their own private movies that are 10x better.