https://support.google.com/websearch/answer/7631341?hl=en
and does not have anything more to do with "anonymous" searching
It clearly says that it provided provided users with anonymous search, which gives the impression of something like DuckDuckGo or Startpage. But that's not what's happening, and I think that's worse than your original complaint.
https://web.archive.org/web/20100524223335/http://www.google...
> Note that SSL search does not reduce the data that Google receives and logs when you search, or change the listing of these terms in your Web History
Searches performed at encrypted.google.com (not just google.com with SSL) were not available in any user-facing capacity in one's Google account. It did not store the search queries in user-facing history, and did not use those terms for future search suggestions.