I'm not too attached to my conclusion, in fact I hope it's not true, and have also thought about what you said. But I am convinced that, eventually, humans will be capable of making autonomous AI advanced enough to "replace" them, and I am NOT convinced that humans will choose not to - especially given the fact that over enough time people will slowly allow AI to control more and more of their lives and the world. Then the next generation of people will grow up accustomed to this level of invasiveness and think it normal, and trade off more of their freedom to AI in exchange for more convenience and comfort.

As for the concern about whether there will be enough useful work to keep everyone paid. Eventually the answer is definitely no in my opinion, just a matter of how far out that is, but I don't think whether there will be enough work is a meaningful question in that world. If AI is good enough to replace human work then the work is still being done - in fact MORE work is probably being done, and therefore more goods/resources(post-scarcity as you said). It's a question of whether humans can distribute those resources fairly - this question and problem remains the same whether people need to work or not. We already have more than enough resources to keep everyone in the world fed and comfortable, assuming we don't destroy the planet this will only be more true when the AI work force comes into play.

It's easy to assume that in such a world there will be enough resources for everyone to live very comfortably while the higher class still has extremely excessive control over resources, and as such it's not likely that greed(the main obstacle to a fair outcome) would have to come into play, as the rich and power-hungry can have everything they want without having to allow poor people to starve to death.

Unfortunately I'm not convinced that assumption is valid either though, because of the fact that the psychological factor driving the greed of the ultra-rich isn't the desire for material possessions and wealth in itself, but to have "more" - more stuff, more capital, more power, than others. They don't just intrinsically love 100 million dollar yachts so much that they choose to buy 3 of them instead of, say, saving the lives of millions of starving children. What they love is the inflation of their ego and the feeling of power and superiority. If middle-class person suddenly had 100 million dollar yachts those people wouldn't be satisfied with their own anymore. Because of this, I think the ultra-rich and ultra-powerful, who of course will be the ones in power and who will have the ability to influence how resources are distributed in a post-scarcity world, will be motivated to keep the lower classes "lower", in order to maintain their ego and satisfy their power craving(though they will of course justify it in less crude ways).

To make my point more simply: If Jeff Bezos could snap his fingers right now and magically make every single person on earth exactly as rich as he is, give them all the same resources and material possessions, at no cost to himself, I am quite convinced he would not do it. This is a simpler version of the exact same decisions those in power will have to make over the next centuries - and in their case it will probably be easier to justify to themselves as it won't be so black and white as denying fortune to billions of people at no cost: that will be exactly what they're doing, but over the course of many small decisions that is each justifiable in it's own way, such that they never have to realize that that is exactly what they're doing