Tor has its flaws and criticisms, but it's really not on Kagi to fix them. With the combination of tor and their privacy pass, Kagi has gone further in allowing their paid users access to their services than anyone else.
Disclaimer: Not associated with Kagi in anyway other than being a very happy user.
(Privacy Pass in fact doesn't make sense outside of an anonymizing transport, which makes the current announcement an exercise in marketing, at best)
This kind of thinking is pervasive in the discussion of privacy enhancing technologies. It might not make sense against the most sophisticated attacker, but it lays the groundwork of a complex system that will be able to do so.
Allowing more users will provide herd privacy at the token generation phase. Searches being decoupled from user account primary key offers privacy in all kinds of scenario's, comparable with a browser private tab.
> This kind of thinking is pervasive in the discussion of privacy enhancing technologies
It is in RFC.
Origin-Client, Issuer-Client, and Attester-Origin unlinkability requires that issuance and redemption events be separated over time, such as through the use of tokens that correspond to token challenges with an empty redemption context (see Section 3.4), or that they be separated over space, such as through the use of an anonymizing service when connecting to the Origin.