As a privacy-oriented search engine, I feel that the lack of an anonymous method of payment is Kagi's biggest weakness. I have spoken with people who would be willing to pay for a search engine, but don't want to pay for Kagi because it means all their searches can technically be associated with their real-life identity. And while we know Kagi doesn't need to track their users to keep the business going because they're getting money directly from them, the fact that it is still possible should still be a cause of concern. In an ideal world, we shouldn't have to trust the companies, whose services we use, to not misuse the information they get about us.
Now I will attempt to address some of the counter-arguments I have seen in this thread:
Cryptocurrency is not actually private
Bitcoin most definitely isn't private, the only reason it is still used is because it is the original cryptocurrency that everyone knows. I recommend using Monero instead, which is pretty much the only cryptocurrency that is used for payment on the internet aside from Bitcoin, and that is not because it has a big name but because it is actually a private cryptocurrency.
Not many people will actually purchase using cryptocurrencies
While this is true, I still think it is important that it is implemented, because it gives the user the option to remain completely anonymous if they want, instead of being forced to disclose their personal details in order to use the service. While I'd definitely be one of the few who pays with cryptocurrency, even if I weren't, I'd still rather give my information to a company who gives me the option to remain anonymous than one that doesn't, because it proves they actually care about privacy and anonymity.
It will take a long time to implement
I still think it is worth it. To me, this is the single most important feature Kagi can implement right now, and I won't expect it to be out tomorrow - I'm fine with waiting for it.
Kagi is a great search engine because it is the fastest, the most costumizable, it has the highest quality of results, but it is not the most private. I hope that will change at some point.