I would think that a universe where there were no scarcity would be a place where the human mind isn't wired up for.
We are all biological animals and need to compete by our genetic programming.
Having everything available at any time for replication would be like having enormous wealth- probably even better.
The problem is that people who are enormously wealthy do only a few things:
1. Try to become wealthier.
2. Become decadent/self destructive (especially if the wealth was given to without being earned).
3. Use the wealth to help others- charities, etc.
4. Use the wealth to push boundaries -science, exploration, etc.
If you have eliminated items #1 and #3 (unless I'm missing more categories), it only leaves #2 and #4.
#4 would be showcased in Star Trek, but what of #2?
We've all seen what happens to people who win the big lotteries, I haven't seen one go down path #4 yet.
Quite true. Nobody knows what a post-scarcity society would look like, how it would work, or if we'd even survive it. Although the flip side is that our biological competitive nature, for space, resources, sex, and just plain dominance (to better ensure the first three) colors a lot of our own thinking about the future, and what other players will do.
"ALIENS GONNA EAT US/DESTROY US/ENSLAVE US!"
"AI GONNA EAT US/DESTROY US/ENSLAVE US!"
Etc. etc. etc.
Despite the effort invested in pointy ears and bad haircuts to put Vulcans on screen, nobody that I'm aware of has ever really looked at ANY facet of our existence from a purely logical or game-theory standpoint to make rational guesses as to what will happen in terms of aliens, AI, or post-scarcity society. It's impossible to truly stand outside our human frame of reference and make unbiased calculations on these things.
Although that goes back to my even BIGGER criticisms of science fiction, especially on screen, that it is nowhere near inventive or truly speculative enough to cope with ANY of the "big ideas".
Five hundred years in our future, with only one minor setback around the 21st century with a nuclear war? Matter/Antimatter energy? AI, genetic engineering, FTL?
Honestly, we would should probably look more like the "Q", or maybe the monoliths of 2001: a Space Odyssey, than the Federation.
It's not exactly a great metric, but if you look at our computers, phones, tablets etc. and compare them to STNG's set designs of just 25 years ago, you can see how our "future" is arriving faster than a TV show full of writers and prop makers with a budget of millions could imagine or depict in a convincing manner.
One Sci Fi author of note, William Gibson actually recognized the problem, and "gave up" on writing cyberpunk as Sci Fi, and pretty much now just considers his works to be contemporary techno-fiction set in "today" more or less.
Of course, if you genuinely try to recognize this fact, and write for it... it absolutely KILLS every Sci Fi franchise of note that's at all interesting. Otherwise all Sci Fi would read like one of these two scenarios:
1. Humanity was stupid and wiped themselves out already. So there's really not much to tell. The end.
2. There was some sort of a problem. Well, not exactly a "problem" per-se, but a
potential problem, because what passes for "people" in the future were smart enough to see it coming, and did something about it in plenty of time because they were incredibly powerful, wise, and nearly omnipotent. So the problem never actually happened. The end.
"1.5" scenarios, somewhere in-between, like Star Wars, Star Trek, Firefly, BSG.. you name it. It's wishful thinking in the extreme just so the writers have a universe or place to play around in.