What about preview suggestions? A lot of people probably (ab)use search because they only half remember an URL they would easily recognize if they'd be given the option to click on it in a dropdown.
Also, Google has recently expanded their preview suggestions. If you type "Orlando Bloom" you will see the name with a small pic in the preview options. While with Google, this initiates a Google search, Kagi could take a different approach and send users directly to a popular information source (like Wikipeda). As long as it's clear where you will be heading, this could be a cool feature and a cost-saver all in one.
EDIT: Preview suggestions could also be configurable or simply based on what is set up under "search with..."