A simple problem with search engines is that you have to trust that they will not build a profile of search queries you submit. (Without Tor or e.g. homomorphic encryption, that is.)
Suppose we put together a search engine server with a use policy that permits constant queries being sent by paid customers.
The search engine's client transmits, at some frequency, generated search queries (e.g. markov, ML-generated, random dictionary words, sourced from news, whatever; up to you) in order to intentionally obscure the real search queries performed by customers. In other words it pretends to be a thousand contradictory personalities, nationalities, genders, races, hobbies, etc.
How difficult would it be to generate enough queries to hide yourself in the data?