But OP is right that this would actually be serving their target demographic less well than serving everyone the same results regardless of context. The fact that the results don't know where the user is is reassuring for the kind of user who wants to use a privacy-oriented search engine, regardless of whether localized results could technically be provided in a privacy-preserving way.
These things are not mutually exclusive. Allow me to specify a city or state or county or country or zip code as a bang in my search and show me good results based on that. Both problems immediately solved. I wouldn’t be any more or less reassured about a search engine’s privacy stance if that feature was offered to me. This is a feature I can absolutely use in a private way (I can do that search over tor or a vpn with two hops if I so desire), and it gives me the control over what I provide the search engine and how and when.
Right now search engines don’t provide an interface for good location aware searches that you can manually specify - you have to let them build a shadow profile on you via all sorts of privacy violating fingerprints or just give up location aware searches altogether. There’s no reason it has to be that way though.
> These things are not mutually exclusive. Allow me to specify a city or state or county or country or zip code as a bang in my search and show me good results based on that. Both problems immediately solved.
Do you actually find that attaching your location to the end of the query doesn't work? I don't do it naturally, but when I do do it I'm rarely disappointed.