Privacy seems like it would be a major issue. As a litigant, I would not want the opposing side piping my case information to a third party and having this information used to train the AI for future cases.
AI could be very useful for helping pro-so litigants prepare documents. I imagine with this use case as well as the oral argument use case, judges are also worried about low quality output wasting the court's time.
Self-representation is frowned upon, "a person with themselves for a client has a fool for a client." But, where in the UK system is it disallowed, unless you are a repeated, "freeman of the land" nonsense spouter?
Off the top of my head: depending on the jurisdiction there are several important legal documents that you are disalllowed from filing yourself and the judge is allowed to reject you with or without reason
Self-representation is frowned upon and mostly disallowed. Lawyers are expensive. I'd genuinely consider having ChatGPT fight for me.