It wouldn't be cool because it would still hand your data to Google.

I assume Google was just a placeholder for a search engine in the example. And you'll surely need some service to search the web.

I don't know about that. When I hear people reference "Google" it seems to me they do mean Google. Similar with "Claude".

We’ve got the whole post to parse, though.

The idea is obviously applicable to other search engines.

People still use “Google” as a synonym for “online search.”

Yes, and IME it also is true that "online search" means in fact google.com. And there's no distinction for search results and reading the google AI summary.

It could anonymize the data, at least.