I think privacy is massive but that leads to how will search engines that focus on privacy make enough money? Google offers a good search engine and a heck of lot of cool free software, all payed for by ads. Frankly, I don't mind targeted ads as they're far less annoying than random ads. I'm into the outdoors and tech and even went so far as to go into my Google settings and adjust it. No, I don't like Tango. What was that about in my settings?
So I'm not even 100% convinced that the trade offs in going to a completely private search experience are worth the costs. I don't know.
What are some other problems a search engine company could focus on? I'm not even sure what the top concerns are of users that would inspire them to migrate from something that is pretty damn good, frankly.
Remember Altavista (and similar search engines from the era?) it worked, but everyone was using the same approach so you got the same results when you searched for a given word... Then Google arrived and the quality of their results looked like magic.
In terms of "user experience" today does resemble then: Bing, DuckDuckGo... They return a subset of what Google finds, not something qualitatively better.
Result quality has not really improved, all the while: more and more content is in silos that are not easily searchable. Spam/SEO/trust in content remain a problem, thus many people rely on social recommendations for content (which has its own problems). More and more content is in non-textual forms. Google (sometimes vastly) prioritizes content on their own platforms.