It's not at all clear how easy it is to obtain a user's search history, when users don't explicitly log in to those services (e.g., incognito/Private browsing), and don't keep history on their local device. I've been trying to find a
single example of a court case where this happened, and my Google/ChatGPT searches are coming up completely empty. Tell me if you can find one.
The closest I can find is "keyword warrants" where police ask for users who searched on a given term, but that's not quite the same thing as an exhaustive search history.
Certainly my personal intuition is that historically there has been a lot of default privacy for non-logged in "incognito" web search, which used to be most search -- and is also I think why we came to trust search so much. I expect that will change going forward, and most LLMs require user logins right from the jump.
As far as the "I can see no reason" why LLMs should be treated differently than email, well, there are plenty of good reasons why we should. If you're saying "we can't change the law," you clearly aren't paying attention to how the law has been changing around tech priorities like cryptocurrency recently. AI is an even bigger priority, so a lot of opportunity for big legal changes. Now's the time to make proposals.