The catch is that many judges lack the time, energy, or willingness to not only read the documents in detail, but also roll up their sleeves and dig into the arguments and cited authorities. (Some lack the skills, but those are extreme cases.) So the plausible argument (improperly and unfortunately) carries the day.
LLM use in litigation drafting is thus akin to insurgent/guerilla warfare: it take little time, energy, or thinking to create, yet orders of magnitude more to analyze and refute. (It's a species of Brandolini's Law / The Bullshit Asymmetry Principle.) Thus justice suffers.
I imagine that this is analogous to the cognitive, technical, and "sub-optimal code" debt that LLM-produced code is generating and foisting upon future developers who will have to unravel it.