The engine isn't the problem. The indices are. Google has massive amounts of data to index over, and they've been collecting it in useful form for longer than anyone else still in the game.
My main point still stands though. How is there not anyone willing to take another shot at competing here, the world's love affair with Google is no doubt over. DuckDuckGo is relatively popular even though it doesn't seem to offer anything truly original in the search space.
A truly new way to search that helps fight the monopolistic search behavior would be very useful. It feels like something Mozilla foundation would be into if they didn't receive so much funding from Google.
Cliqz did and they lost.
Search data isn't neccessarily user data but what good do the particulars of search data for long defunct domain names provide them? The only thing relevant now are any current archives to search.
Google still reigns supreme in the text search department though.