It's not that Kagi is expensive at all. It is that your streaming services and premium e-mail service are incredibly cheap. Can you name a few things which you can purchase in your local supermarket that brings you the same value for $10?
the value of a paid online service is not "how useful is it in a vacuum?", it's "how much more effective is it than a free competitor?"
kagi's value is "how much more effective is it than using google with an adblocker?"
getting the value of the only search engine in the world at the supermarket for $10 would be a challenge. getting the value of "improved search results" is absolutely trivial. you could keep yourself alive for many days with $10. for $0 you can use google with an adblocker.
How are you going to do that math? I'd say it's at least twice or three times as effective as any free option. So at $10 it's an absolute bargain. But hackers will say that $10 is an infinite multiplier of zero, so you should always be "rational" and use the free service.
I'm not at the stage in my life where I don't have to count pennies for my food budget, and neither do most people. You're also comparing supermarket food with a vacuum of a person who is about to starve to death. I mean in real life, assuming you're not suffering from atrophy, what can you buy in the super market that brings the same value? This is of course assuming that you have an interest in better search quality – which not everybody has.
You could also argue that a wooden log is worth more than $10, because you can keep yourself from freezing to death by burning it. Then the value is infinite.