@benjaminradio i'm not sure what kind of preferences you mean. i guess those personal rankings of websites and such? you can use kagi without those, they recently introduced kagi privacy pass so you can use their service anonymously.

https://help.kagi.com/kagi/privacy/privacy-pass.html

you don't have to use their AI features either. my plan only gives me that quick answer feature when i explicitly request it, i don't even have access to their full fledged assistant which would also preserve the context. privacy wise the assistant sounds pretty similar to duck.ai to me