You cite one case for LLMs, but I can cite 250,000 a year for licensed doctors doing the same https://pubmed.ncbi.nlm.nih.gov/28186008/. Bureaucracy doesn't work for anyone but the bureaucrats.
Unless the judge has you examined and found to be incompetent, they're most likely to just tell you that you're an idiot and throw out the case.
That actually supports the use-case of collaboration, since the weaknesses of both humans and LLMs would potentially cancel each other out.