No answere. Oh well. 🤷
Meanwhile, I found and adapted a repository with CSS to hide most of #Kagi AI stuff.

/* Hide most "AI" stuff */
/* Inspired by https://codeberg.org/zerodogg/kagi-no-ai */
#assistant,
#accountContainer a[href^="/summarizer"],
#accountContainer a[href="/fastgpt"],
._0_summarize_link,
hr:has(+ ._0_summarize_page),
._0_summarize_page,
._0_discuss_document,
.search_form_box:has(#searchBar:placeholder-shown) .newsRedirect,
.auto_item:has([*|href="#bolt"])
{ display: none !important }

I also found out there's an option to disable the assistant for children. So it seems very doable if only they wanted to give the option to all their customers.

@pluralistic