Because Kagi is doing what Google was in 2008; taking a query and returning links as results. Indexing the web doesn't need an LLM.

Google needs an LLM because they have a business need to answer the question for you, thus keeping you on Google.

It's not the same. Kagi is trying out multiple products including ones that depend on LLMs (eg. a summarizer). But they're not changing the core web search product by inserting these alternate features. If they do, I'll cancel my subscription and I think others will, too. Since Kagi is supported by user subscriptions instead of ads, they'll have to pay attention to that or collapse.