This is particularly useful in the context of a privacy-respecting paid search engine, where the Server wants to ensure that the Client can access the services, and the Client seeks strong guarantees that, for example, the searches are not associated with them.
Hoping to be constructive: how do you think search engines should operate? Or maybe how would you like one you consider "good" to operate?
Also wondering how you see something like Privacy Pass that Kagi announced recently: https://blog.kagi.com/kagi-privacy-pass