Manna is the title of a science fiction story that describes a near future transition to an automated society where humans are uneconomical. In the later chapters it describes in some detail a post-scarcity society. There are several problems with it however, the greatest by far is that the author seems to have assumed that "want" and "envy" are primarily tied in material needs. This is simply not true.
I would love to live in a society with material equality on a sufficiently hight standard, I'd however hate to live in society with a enforced social equality, simply because that would override my preferences and freedom to interact or not interact with whomever I wish.
Also since things like the willpower to work out (to stay in top athletic condition even!) or not having the resources to fulfil even basic plans are made irrelevant, things like genetic inequality or how comfortable you are messing with your own hardware to upgrade your capabilities or how much time you dedicate to self-improvement would be more important than ever.
I predict social inequality would be pretty high in this society and mostly involuntary. Even a decision about something like the distribution of how much time you use for self-improvement, which you could presumably change later, there wouldn't be a good way to catch up with anyone (think opportunity cost and compound interest), unless technological progress would hit diminishing returns and slow down. Social inequality would however be more limited than pure financial inequality I would guess because of things like Dunbar's number. There would still be tragedy (that may be a feature rather than a bug of utopia). I guess people would be comfortable with gods above and beasts below them, that don't really figure in their "my social status compared to others" part of the brain, but even in the narrow band where you do care about inequality would grow rapidly. Eventually you might find yourself alone in your specific spot.
To get back to my previous point about probable (to me) unacceptable limitations on freedom, It may seem silly that a society with material equality would legislate intrusive and micromanaging rules that would force social equality to prevent this, but the hunter gatherer instincts in us are strong. We demand equality. We enjoy bringing about "equality". We look good demanding equality. Once material needs are met, this powerful urge will still be there and bring about signalling races. And new and new ways to avoid the edicts produced by such races (because also strong in us is our desire to be personally unequal or superior to someone, to distinguish and discriminate in our personal lives). This would play out in interesting and potentially dystopia ways.
I'm pretty sure the vast majority of people in the Australia project would probably end up wireheading. Why bother to go to the Moon when you can have a perfect virtual reality replica of it, why bother with the status of building a real fusion reactor when you can just play a gameified simplified version and simulate the same social reward, why bother with a real relationship ect... dedicating resoruces for something like a real life space elevator simply wouldn't cross their minds. People I think systematically overestimate how much something being "real" matters to them. Better and better also means better and better virtual super-stimuli. Among the tiny remaining faction of remaining "peas" (those choosing to spend most of their time in physical existence), there would be very few that would choose to have children, but they would dominate the future. Also I see no reason why the US couldn't buy technology from the Australia Project to use for its own welfare dependant citizens. Instead of the cheap mega-shelters, just hook them up on virtual reality, with no choice in the matter. Which would make a tiny fraction of them deeply unhappy (if they knew about it).
I maintain that the human brains default response to unlimited control of its own sensor input and reasonable security of continued existence is solipsism. And the default of a society of human brains with such technology is first social fragmentation, then value fragmentation and eventually a return to living under the yoke of an essentially Darwinian processes. Speaking of which the society of the US as described in the story would probably outpace Australia since it would have machines do its research and development.
It would take some time for the value this creates to run out though, much like Robin Hanson finds a future with a dream time of utopia followed by trillions of slaves glorious , I still find a few subjective millennia of a golden age followed by non-human and inhuman minds to be worth it.
It is not like we have to choose between infinity and something finite, the universe seems to have an expiration date as it is. A few thousand or million years doesn't seem like something fleas on a insignificant speck should sneer at.