> I understand that they claim to store no user data or associations etc, but honestly, it's just their word.
My guess is that if they are found to do so, then they open themselves up to lawsuits. Not collecting data isn't merely a perk - it's practically the reason Kagi exists.
Another big reason not to keep this stuff is just the cost of dealing with requests from law enforcement. At some point you start getting them.
If you don't have any logs you can just always say the princess is in another castle, since you can't provide data that doesn't exist.
If on the other hand you do have the requested information, you need to determine the validity of the request, and then extract the data; or refuse to comply and possibly put yourself at legal risk. For a smaller business that's probably a can of worms you'd rather avoid opening.
My guess is that if they are found to do so, then they open themselves up to lawsuits. Not collecting data isn't merely a perk - it's practically the reason Kagi exists.