Also, an interesting example: in English litigation (where, broadly, loser pays unlike America where each side pays), maximising billable hours is not always a viable strategy for anybody if those costs aren't recoverable on success. Someone involved in large-scale commercial litigation involving disclosure of millions of documents who doesn't use algorithmic document classification (now pretty broadly accepted as normal) potentially runs the risk of a judge determining that the costs of going through all the documents by hand isn't recoverable. Insurers/litigation funders aren't going to want to risk padding the costs so much that the judge prevents them from recovering their stake in the litigation.
Customers using their own LLMs: yep, they might do that. I think the pitch from the legal LLM providers is "we've got legally trained people doing RLHF to make it more accurate" mixed in with "also we've got a partnership with Lexis/Westlaw/etc. so we can do legal research that's better than what's on the open web", with a little bit of "if you get sued for professional negligence, 'I used the legal AI thing that's built into Westlaw' is gonna be more convincing to a judge and jury (and your insurance company) than 'I used ChatGPT, yes, like the app you've got on your phone'...".