Even if it were a process as invasive and painful as getting a bank account, it would remain the only technology that enables users to get a search account privately (since Kagi says cash is not scalable for them). Given the level of snark and off-topicness, I presume you don't actually expect me to answer the question with dozens of different methods.
This is a company that claims over and over that they are privacy-respecting, but are running a service that unnecessarily collects your real ID via credit card, otherwise you can't do searches. After seeing what happened to Google, I am shocked that people like you are so dismissive toward me for trying to hold them to account and caring about this issue. Yes I react with religious fervor at this issue - privacy. This is an age where companies are handing over information to convict people for seeking abortions even in the US.
If you have another solution then please share it.