There's a clear search engine improvement which I'd love, and my friends would love, but I think it's not yet technically possible. (the tech to do it exists, but it's a big engineering challenge to actually build it in an economically viable way).

A way to search (public, private) documents without leaking ANY information (beyond possibly "I did a search") to the operator. DDG's "trust us" security policy doesn't really go far enough. A mix-net anonymizing your query is the best option now, but it's insufficient. Just knowing someone in the world is searching for a specific piece of information is itself highly actionable in some contexts.

USG and other highly security conscious entities accomplish this by having the full search corpus onsite and running the searches on their own hardware. There's Google Enterprise (which was the most red-headed stepchild product I've ever seen from Google) too, and there are commercial ways to buy the crawl and run an engine on top of it, but this isn't really something even Fortune 500 companies do.

Basically, either a permanent "personal google appliance", potentially hosted in the cloud using some tricks, or a way to spontaneously instantiate a google each time you want to do a search.

Probably the way to do this is to write some interesting sci fi novel featuring the dangers of public search leaking, and also wait for some interesting prosecutions which use search data as evidence.

You could actually still do advertising this way, too; just requires some tricks.