I think that Search Engines have been mostly commoditized, and that the company with the biggest budget pretty much wins the game.
However, maybe there's space for a different kind of search engine.
Would you build a new one today? If so, what would make it different from anything else?
A new search engine would just drop the top x sites from its index, and be aggressive with dropping sites. Blog spam? Link farm? Quora? Pinterest? Wikihow? Don't index them at all. A Shitty wordpress site that's just copying stuff verbatim from other sites? Drop them. Over engineered SEO? News sites? Fake news? Satire sites? Don't bother with them etc. (or maybe put a clear disclaimer in the case of satire sites)
Make search about what it's supposed to be, discoverability.
There are so many golden sites out there to be discovered under the absolute cruft Google and the like bury us in. And the new 'you.com' isn't any better because they're just getting their results from Bing, and they've been caught taking their results from Google!
Google keeps competition away because it is able to generate much more revenue per search than competitors. Worse results translate to worse revenue (e.g. if the #1 result was always the best, why look at the ads?)
If somebody else could make the money work they could definitely give better search results.
I'd design it the same way I designed the text editor I'm making ( https://twitter.com/LeapJosh/status/1455511983512436737 )
Hit the minimums. Be irreverent, elevate the ordinary.
Manifest intrigue. If you can't do that, at least make your users feel weird.
Curating content for by subject matter and then aggregation and spidering the resulting content would yield better quality rather than quantity.
Decentralization with cooperative subscriptions would provide a good search population rather than the unfiltered firehose of the current web.
Honestly I’d be happy with a google that just let me quickly hide results from certain sites.
What makes it different is business model that aligns incentives and obsession with the user experience.
Turns out they are cheap to build and operate, and and an endless font of interesting engineering challenges.
Niche search engines or metasearch engines like Tripadvisor and Skyscanner are welcome because they come in handy where Bing or Google do not or in another words they are more specialized for certain niches than general internet search engines.