This suggestion may be related to this thread in some way. I gave some ideas about queries to official websites (and others like documentation websites) in a reply.
This suggestion could be broadened. Sometimes a user wants a website but does not know the full URL, especially the TLD (see the Inkscape example). However, many users are accustomed to using Google to get to frequently visited sites like YouTube, Twitter, etc., rather than typing it into the browser bar and using the history (or better, a bookmark).
One idea to solve this costly problem could be to implement a toggle that allows searching only in Kagi's internal index, since a full index search is unnecessary in such cases. Also, a results page with only one entry might be awkward.
Several ideas have been suggested here, such as crawling Wikipedia to get the URLs of official websites. Another option might be to index the most visited sites (like the top 1 million) in the hope that this would cover programming sites. It might also be possible to get a list of all registered domain names, so that at least a lot of home pages could be indexed (this is a problem for subdomains, though). There are probably other ideas, such as indexing DMOZ entries.