Search is really important to me, and it isn't just about looking up businesses or Wikipedia pages. I read lots of academic papers and just want it to be easy to separate the wheat from the chaffe. Kagi makes that really easy with its lenses. Sure, Brave search has something similar, but I like Kagi's interface better and having to pay them gives me the sense their service won't just be deprecated or significantly changed at the whim of a CEO trying to satisfy advertisers or whatever. Having insight into how many ads and trackers on a page is nice too, as well as being able to demote and block certain domains. It's nice that I can block a domain and it's also blocked on my phone.
What's especially important to me is the ability to wrap my queries in quotes for literal string matches. Granted, no search engine is perfect at this anymore because the web has become so huge, but Kagi seems to be the only search engine I use that gets string matches right more of the time and doesn't give me fake results when there are no actual matches. That's what pisses me off about The Google. And though I once used DDG, I found that the quality of search started getting worse and now it seems like quotes barely even work with that search engine now.
I hope Kagi succeeds. It doesn't need to compete with The Google. Just be good enough for those willing to pay for it.