It's the only mainstream AI service that requests this information. After a string of security lapses by many of your competitors, I have zero faith in the ability of a "fast moving" AI-focused company to keep my PII data secure.
There's also been a spate of AI companies rushing to release products and having "oops" moments where they leaked customer chats or whatever.
They're not run like a FAANG, they don't have the same security pedigree, and they generally don't have any real guarantee of privacy.
So yes, my privacy is more valuable.
Conversely: Why is my non-privacy so valuable to Anthropic? Do they plan on selling my data? Maybe not now... but when funding gets a bit tight? Do they plan on selling my information to the likes of Cambridge Analytica? Not just superficial metadata, but also an AI-summarised history of my questions?
The best thing to do would be not to ask. But they are asking.
Why?
Why only them?