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.
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.
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.
Supposedly they are not doing it because of advantages of associating your payment method and searches.