It's not the email alone that is valuable. It is the email paired with your search history that is valuable. If you remove the email, and instead tie to to a uuid, the search history is much less valuable. This is the basics of data minimization.

Which, again, is fine if Kagi doesn't want to do. They just shouldn't pretend that there isn't any other solution other than email, because there is.

That is not what I said. Hundreds of data breaches where emails have gotten leaked and there have been no real consequences for the offending company so from a company perspective, email is not data that carries any real liability.

It certainly can be when it is tied to other data. For example, your entire search history.