The cool thing about Kagi is, that, while it also offers a ton of really good LLM features, those are all optional, and the user can configure them for their account.
If one just wants web search, one can set all LLM features to disabled by default - such that they are hidden behind buttons. If one wants to have certain LLM features enabled by default, that's possible too.
In other words, you get exactly the experience you want.