I've done 20 searches this month (I haven't switched it to default) and it says I have incurred $0.25 (between $0.01 and $0.02 per search) so it would seem that it's very expensive for them to provide results at the moment. It would absolutely be unsustainable at a few dollars a year given these consumption numbers.
Lets say you search for "Photo Of A Mother" * Then you click "images" * Then you click "Sort by Recent" * Then you click "Licence -> Public" * Then you click "Size -> Large" * Then you click "Size -> Extra Large" *
Every time I have put a star in the above is a time where you would be charged a search (so the above would be charged as 6 searches). It's the same thing with switching to news, applying filters, blocking a site or boosting a site etc - I've validated this on my Kagi account by clicking actions and seeing what it does to the billing, and just by using the search engine and using the lenses feature for example you can quickly rack up loads of searches.
Now let's say you search for an error while you program, visit the first site, it's not got what you want so you click the back button and then visit the second site, that's not got the right answer so you click back and visit the third site... That's currently counted as 3 different searches rather than 1 search. If you open them in different tabs it's counted as 1 search though.
And with all this then you are suddenly over 25% through your daily allowance on the $10 plan. Even choosing to 'block' a site in the search charges you to block it. They are talking about charging $0.015 per search if you go over-quota (which is something like 20 searches on the $10 plan), but as far as I can tell if you are using it moderately heavily you will blast part the 20 searches and could end up with an eye-watering bill.
I think the team are great, and when I was on discord they were really receptive, but I ended up giving up on Kagi after trying to use it as a daily driver as I figured they wouldn't be able to find a good enough monetisation strategy for my level of usage (after hearing discussions in the pricing channel). The product is good, it's just that they can't offer it at a price I can accept (and I suspect they can't offer it at the moment at a price that the market can accept, unless they can reach a deal on API licencing or roll their own search).
It IS hard to get results as good as Google at a price where people are willing to pay for it.
IMO I think the issue with Kagi is that their current architecture has made it easier for them to get great results (as they are just taking their results from Google + Bing and adding their own special sauce) but it makes it much more difficult in the long run to be cost-competitive.
Their nearest competitor (Neeva) does offer $5 a month search, has a free tier, and rolls their own engine, so I don't really see how Kagi's current model is sustainable unfortunately (but maybe they will be tremendously successful and I will look back at this post and feel silly!).