The difference in privacy I see between Kagi and Google is that Kagi requires me to have a signed-in account to search, and Kagi accurately associates more valuable information with a signed-in account.
Surely you can. You can use blind signatures, it's like issuing anonymous tokens in the style of David Chaum digital cash. Or you can just use existing cryptocurrency.
Supposedly they are not doing it because of advantages of associating your payment method and searches.
Maybe Kagi could offer a more privacy friendly "fill a wallet with crypto and we'll deduct a certain amount per search" option that doesnt require user billing data.
Im not a current user but would be more likely to test it if available.
You have to pick one. And you can’t really fault Kagi for providing the one when the other is already “adequately” covered by Google.