Vlad
So the question to ask is does Kagi have any incentive to disrespect your privacy (eg mine/monetize your data). The answer is no because people pay for Kagi with their wallet, not their data.
I want to emphasize again that this isn't going to assuage people's privacy concerns. I'll also emphasize that I do believe you, and that Kagi is not currently harvesting or selling anyone's data, and that you have no intention to ever do so. I routinely trust private companies with data because they have a clear business strategy that allows them to make a profit off of actually selling their service and not their users. I do understand the point you're making.
But the number of cases where a website or service has done a 180 flip on privacy for one reason or another in order to sell out their users is so numerous now as to practically be a cliche. There's a bunch of ways this could happen even if you personally never change your mind. What if someone legally takes over the company out of your control? What if a government forces you to? What if an employee goes rogue? What if you get hacked? What if someone makes an honest mistake and causes data to accidentally be leaked? All of these have happened to other companies.
Privacy conscious people have learned from experience that the only way to avoid this is to avoid putting trust in companies altogether. And that's what we're asking you to allow us to do.
The best way, and perhaps the only way, you can ensure that this won't happen is to not have access to that data in the first place, and to do so in a way that is plainly evident to your customers. If you provide a way of creating an anonymous but still paid for account using some method (be it cryptocurrencies or blind signature / zero-knowledge tokens or something else) then we don't need to trust you and take you at your word. There'd be no way for there to be data that could be leaked in the first place. And because search engine data is some of the most sensitive data of all — looking into someone's daily searches can potentially tell you more about them than even their email or financial records — it's that much more important that we be able to know that we're keeping our data under our own control without requiring any trust.