Vlad I encountered this issue today. Looking for information on something very specific (orthopaedic thumb splints) Kagi's 25-30 results just weren't enough. I had to swap back to Google for what I needed.
It's not because I was looking for one good result that was buried three pages deep. What I needed was to find at least 20 different pages, of different manufacturers and retailers. Most of them weren't on Kagi's single results page.
If your use case is "the user wants to find the best link, Kagi will have it on the first page", then the Kagi model works. But once in a while we need to do a search where we want to look at dozens of results, for legitimate reasons, not just browsing because we are bored or distracted.
In fact I probably cost Kagi more because I did about half a dozen fresh searches with tweaked keywords before I gave up and went to Google.
With respect to the cost issue, if you use a design pattern to discourage users from casually clicking more, I wonder how many extra requests you would actually see... is it possible it would be insignificant?