I do think LLMs have their place in search and I think the Kagi approach feels a lot better than Googles'. Kagi doesn't inject LLM results anywhere, but they've been making LLMs accessible in their search interface for a long while - this being the most evolved version of that effort. I am not totally sold on everything they are doing but I hate their integration of LLMs the least.
Kagi's auto summary feature when you add a question mark after your query is absolutely excellent.
It essentially summarizes the top search results for you, leaning in on a strength of LLMs (summarizing) while reducing its greatest weakness (hallucinations).
For me, search integration of LLMs also helps bring together the value prop of paid search. It's not just privacy, it's the skillful integration of a premium information processing service (with built in privacy).