Hey Daniel,
I work at Kagi, Thomas on our Discord. One of our users linked this post so I wanted to give our perspective as well 
Hope that’s ok!
As you mentioned, we do offer crypto payments, but indeed right now Monero isn’t one of the cryptos accepted. It’s not that we don’t want to, it’s that when we worked on the implementation, there were 0 payment providers who support Monero that responded to us to integrate. We also have a non-negotiable requirement, which is that they would need to do all the crypto handling, and just send USD. This is necessary because we’re a tiny team, and we can’t get into the business of crypto wallet handling and FX risk mitigation. In the meantime, for people that want absolute privacy, Monero → BTC/Lightning → Kagi will give that.
As for email as identifier, I believe (but haven’t rechecked recently) that we don’t verify the email’s validity (unlike Privacy Guide 
) which means that in practice you can sign up however you want, and then pay using entirely anonymously as per above. Even if we did, you could still use a throw away email and get the same benefit.
As stated in the policy, we don’t store search queries or results (except for beta users of some features for a very limited period to help debug, and some very short term caching to prevent accidental refreshes counting as 2 searches for our users), so we can’t really retrospectively profile. I understand the concern with regards to “what if Kagi lies about this”, and it’s fair, although obviously that would open us to litigation down the line. How would you suggest we address it so you have more confidence?
The other thing I would want to test thoroughly is the results returned. A lot of these search engines “sound good” but in practice produce poor results not related to the terms.
Our users like it, but the good news is we offer 100 free trial searches if you want to check it for yourself