It seems that Kagi is injecting a system prompt that messes up results and appears in thinking traces when the user has web search disabled. This is frustrating.
Ex: I was asking what a quote in a movie means and the thinking trace showed:
Without web access, I need to rely on what I actually remember of the film's dialogue rather than guessing, and I should be upfront if I can't pin down the exact quote.
...
I'll just answer directly from memory, being clear about my uncertainty since I can't verify with a search.
I see this time and time again and sometimes the less capable LLMs get stuck in a loop thinking about how the web search is disabled instead of thinking about the question that is asked.
This makes using Kagi Assistant without web search enabled a far worse user experience (depending on the use case) compared to other barebones model providers such as OpenRouter.
I expect the system prompt to not have negative information about what the LLMs cannot do. I expect no system prompt injected by Kagi when web search is disabled.
