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?
Captchas are trivially broken and you can get access to millions of residential IP addresses, but phone numbers (especially if you filter out VOIP providers) still have a cost.