Kagi requires for an account to be registered and will charge a monthly rate when it's out of beta, so I don't really think that it'll be a threat to Google.
They don't want to.
https://kagi.com/faq#Google-killer
> We don't want to kill Google :) Google serves a purpose in the world and it did help enable the modern society to exist, with all its marvels and flaws. Heck, it even enables Kagi to exist! > > Think of Kagi as a small, premium brand, providing a very different, tailor-made, search experience.