You still need some sort of unit to track resource consumption, maybe that's the Joule instead of the Dollar, but as long as there needs to be decisions made of the form, which is better/should we do, X or Y, then you need a quantitative way to think about it. Von Mises called this "economic calculation".
I'd consider the primary problems of early-Soviet style allocation economics to be (1) informational (2) computational. Money provides a quantitative (if not nice) solution to these because private economic decisions are intrinsically local, infinitely parallel and they self-aggregate.
Happily, look what happened in the intervening decades: mass connectivity and big data, plus the normalization of data mining over petabytes of raw information.
I think, in other words, that we have reached the point where we can batter down the economic calculation problem with brute force.
Even if you are correct, all that computation still needs to be done in some sort of unit. Money is good because it is abstracted from actual stuff. Joules are actually a bad unit, because how do you value an information product in terms of the energy of the computation it does? Hmm.
You use the natural units of the activity. Tonnes of ore or raw material. Hours of factory time. Joules of energy consumption. Production line machinery MTBF. So on and so forth. It's a lot of data, but nowadays we have tools to work with a lot of data.
No, that won't work. You can say, right now, and people do, "If we spend X building this thing, we estimate Y boost to the economy". You can't say "if we use X tonnes of concrete, we expect Y tonnes of Z to be produced" without the X/Y ratio being money. All money is is a way to abstract the worth of something from what it actually is.
Oh, and you can't pay your workers in concrete either. Or do you propose not paying them at all and just giving out rations to people living in barracks...?
Money abstracts demand-pull from production and supply. But abstraction is a complexity management tool you don't need if you can crunch the raw complexity.
What I'm proposing is a "you want it, you got it" economy, basically, that starts from a premise of equal allocation of resource control (not resource use) and allows unused allocations to be reflowed to the use of those with more ambitious projects, with direct-democratic oversight.
For example, if a hypothetical Elon Musk wants to build rockets (a resource hog activity) then he'd probably end up having to make a public case he was capable of it to avoid being vetoed, but case made, the resource allocations of people who prefer to paint at home or study Tudor history other low-expenditure vocations would be diverted to the rocket project.
No, this would not fall prey to hoarding. Hoarding is stupid and gains you nothing in a post-scarcity economy. You end up with a huge heap of copper or whatever that you aren't using, looking like a selfish idiot and with a trashed reputation that follows you around and makes people not willing to work with you.
What do you think Wall Street is, if not an attempt at "crunching the raw complexity"? It doesn't work and can't work.
would be diverted to the rocket project
Diverted by whom? The "owners" of those resources, or your central planning bureau?
Post scarcity relies on the assumption that if we have more than enough raw materials (and we don't, but let's assume asteroid mining or something), and more than enough energy (fusion maybe) and instantaneous transport of matter (otherwise scarcity exists by the stuff you want being somewhere else) then we still won't be post-scarcity really, because people/civilizations will just take on bigger and bigger projects. There will never be a time when there is no need to make a decision on how to allocate some finite resource to create some outcome by a quantitative means.
Even in Star Trek, someone needs to be thinking, how many planets do we colonize this year? How many starships do we build?
