Why not charge x ct per search. Or rather, x ct per click through. Or rather, x ct per action on a target website? Search = advertisements
A lot of people didn't really like that, so they introduced the $10/mo for unlimited. You can still pay $5/mon for 300 searches: https://kagi.com/pricing
I would probably be paying less if I just did cents per search, but I honestly just like unlimited plans, so personally wouldn't get pay per search.
I'm the type of person who does a Kagi search for "5+7" instead of pulling up a Calculator, so I would rack up pretty quickly.