So if the AI can satisfy everyone's material needs (on some scale from basics to luxuries) all by itself, why would people work?

If people own the advanced robots or AIs that are responsible for most production, why would they be impoverished by them? More to the point, why would they want the majority of people who don't own automated factories to be impoverished, since that means they would have no-one to sell to? There's no law of economics saying that ina a wealthy society most people would starve, rather to keep an economy going in anything like its present form, you have to have redistribution. In such a future, tycoons would be pushing for basic income -- it's in their own interests.