Kagi uses Google as one of it's search provider, so is hardly competing with Google.

In terms of quality search results, kagi is ahead of google. Unless I misunderstand the situation, inferior search result are a natural product of google getting paid by advertisers rather than kagi getting paid by their users. Google won’t be able to get away from using their index to serve up adverts (rather than quality results).

My point is Google gets money when you use Kagi, so they aren't really directly competing with Google.