"I have nothing to hide" is a poor reason to abdicate one's right to privacy. Especially considering how arbitrary and capricious Anthropic is about enforcing Dario's model of ethics and morality.
Especially as the convenience in this case seems quite minor even ignoring the incredibly steep cost, particularly as I do not trust any of the companies offering these services to accept proper responsibility and accountability for failures, even ignoring the privacy issues.
For now with not all agents controlled by advertising engines, and not all content yet designed to honeypot them, today's agents make good headway bush-whacking their way to finding the right information on which to base task work for you.
If the first page of SERPs for anything, and the extra time needed to suss out quality information to inform your work or task doesn't bother you, then this benefit isn't one you'll value.
Put another way:
Today's agents help "cut through" the same maze of value extraction that Silicon Valley (where market share means find a way to tell users your thing is "free"), adtech, and the content-as-ad-scaffolding industry have built over the past three decades. Why waste time wading through all that when your time is better spent building more of it? :-)