The technology proposes a source of labor for the elites so abundant that they will not need to trade their wealth with the eaters.
However much resources you consume, it will be too much to buy for your labor. You will be priced out of existence.
The evidence for this is all around us. As automation of manufacturing has brought former luxuries into reach for middle-class families, those with means move on to consuming items that require more and more labor to produce. "Handmade" scented soaps. "Artisanal" cheeses. Nobody with money wants their wedding invitation to arrive at a destination with machine-canceled postage. It's tacky. Too automated, too efficient. In fact, I bet the ultra-wealthy don't even use postal mail for delivering their invitations, because it's not labor-intensive enough to be tasteful. Private couriers are probably the move. You can see this pattern over and over again once you know what to look for.
There will always be a demand for human labor, because value is a human construction. That said, the rate at which the economy will change because of AI (if the True Believers are to be believed) is probably too fast for most workers to adapt, so you may not be entirely wrong in your conclusion depending on how thing shake out, but the way you got there is bogus imo.
Automation results in centralization of power. It transforms labor-intensive work to capital-intensive work and reduces the leverage of the working class.
You could have a system that distributes wealth from automation to the newly-unemployed working class, but fundamentally the capital-owners are less dependent on the working class, so the working class will have no leverage to sustain the wealth distribution (you cannot strike if you don't have a job). You are proposing a fundamentally unstable political system.
It's like liebig's law of the minimum or any other natural law. You can try to make localized exceptions in politics, but you are futilely working against the underlying dynamics of the system which are inevitably realized in the long term.
As has been seen time and time again throughout history the commoners will only put up with so much and when all else fails and they start suffering a bit too much leverage comes from the end of a barrel.
Note that the stench of inevitability likes to sneak into these discussions of systemic problems. Nothing is set in stone. Anyone telling you otherwise has given up themselves. The comment section attracts all kinds of life outlooks, after all. The utility of belief in some sort of agency (however small) shouldn’t be surrendered to someone else’s nihilistic disengagement.