Vlad
I am mostly referring to GDPR-related and "right to be forgotten" or "defamatory" mentions.
Where persons deal with an issue where your name is e.g. in an online article and you'd NOT WANT it there because it damages your professional reputation.
In my recent case, I had succeeded in requesting removal of my personal information at the website operator side AS WELL AS succeeded with Google to assist in removing specific (defamatory, damaging) search requests for "my name".
For Kagi Search, I'd want to at propose to have to option to ask for "re-crawl", have an option to see "where the result is from" or even request manual intervention to have a person at Kagi decide "blocking" a specific search result for a given search term.