This is a question that's growing on me, the last few playthroughs.
What vote records are currently discoverable make it clear that Athena, specifically, wanted the labyrinth. This was her idea, she moved heaven and earth (literally in the persons of Zeus and Demeter) to make it happen, to the point that she didn't care who could tell she was rigging the trial, and then even demanded a recount which she then adulterated. Why? Why does it matter to her that Asterion have his own private hell dimension forever?
One possibility is the way that a lot of the current scholarship seems to accuse Athens, Athenian historians and poets and playwrights, of skewing the mythological body of Ancient Greece to give Athens a more important place within the lore: Athens, as an inhabited site, is not as old as places like Mycenae, Sparta, Corinth, Arcadia, or especially Crete, but because they were the ones writing the history and doing the theatre contests and establish the academies, the version of ancient Greek history and myth that gets passed to us is THEIR version. The Narrator says as much themselves, cites the Orestia as an example, which ends with Athena talking the furies into "legal justice" rather than "revenge" and inventing Due Process, in Athens, which is ridiculous. So maybe this was an attempt at something like that? Maybe Athena thought, oh, I need the fact that Athens won and Crete lost to be something that everyone gets always reminded of forever, I can't let it be forgotten in the underworld.
Another possibility is that Athena's fallen into Recursion, the same way Hermes does at the (current) end. Setting up a labyrinth with a human master who torments Asterion might be recursive, with the succession of Masters standing in for Theseus. But it's also possible that it's a recursion of the older rivalry against Poseidon: hell, Theseus himself might be a recursion of that. Asterion being of Poseidonic lineage, and part of an actual sacred Bull-Themed lineage, as his underworld trial explains, might be reason enough. The question, though, is if it is recursion, is it DELIBERATE? The recursion Hermes fell into seems to have been partially intentional on his part, he set up the Argoi, which means the first step of his plan to free Asterion was "make the situation more like one of his myths," presumably in the hope that recursion makes it more likely to succeed. So, was Athena trying to accomplish something to which she meant to connect Asterion's punishment? Have him re-enact the labyrinth as a power source? Or, is it possible it's not HER recursion, it's Asterion's? According to Robert he's maybe much more powerful than he knows, so perhaps his recursion, like, gravity well is powerful enough to pull Athena into orbit?
A third possibility has to do with what Robert tells you about Asterion's soul, that it's been "drained" in some way. Now, it's possible this happened at the initial actual killing, something to do with why the Labrys is the way that it is, but it's also possible that draining him and keeping him drained is what the labyrinth is supposed to do? I don't think there's enough material yet to speculate as to why.
The final possibility I can see is that it's something to do with the way mythicals are marginalized in this world. We seem to be dealing with a somewhat... right-wing Athena, let's say, one who emphasizes Law and Order and The March of Progress and Civilization. Humans, then, could be aligned with Athena (every background you can pick, except "speedrunner," is something that falls under her patronage,) and non-humans with Poseidon (since Hermes' vote mentions her grudge against Poseidon's "lineage.") I could see this leading thematically into a mandate that people who are clearly not human are required to remain invisible with the charm and passport system. Whether that means she instituted the first one, just divinely inspired them, or just happens to like them, they do seem to be thematically congruent.
