Instead of send the search query using GET HTTP method, it's preferable to use POST.
This adds more privacy to searches because queries travel encrypted (because of HTTPS) and there won't be any history about your searches in the browser.
This is a feature that Startpage has.
And some browsers, like Vivaldi, support searches using POST from the address or the search bars.
When a user enters kagi.com and performs a search, transparently to the user, the query should be sent using POST.
Or, if the browser supports the feature, the user could configure it to send queries using POST.