I think a click stream isn't necessary, but Kagi is not a good basis for the argument in my opinion.

Kagi is a primarily meta search engine. The click stream exists on their sources (Bing, Google, Yandex, Marginalia, not sure if they use Brave). They do have Teclis which is their own index that they use, and their systems for reordering the page of results such as downranking heavy ad pages, and based upon user preferences (which I love).

https://seirdy.one/posts/2021/03/10/search-engines-with-own-... is a source I would recommend checking out if you are curious.