If there were 10 search engines with 10% of the market and fairly different results then great
I hope this doesn't sound rude. I am not trying to pick on Mojeek, but just the general problem.
I think 10 search engines who all want to index the whole, general web like Google, but with tweaked results, is not the path to breaking the monopoly.
What makes a library valuable on a global scale is that is has a collection that is unique. If I have a library in my town and you want me to travel to another town, your library has to have some books my library doesn't have. The Bibliotheque Nationale is different from the Library of Congress not because they are both trying to collect all the same books, but group them differently on the shelves (though they do that, since they have different cataloging systems). I go from one to the other *despite* the different cataloging methods, not *because* of them.
People will pay for a plane ticket to get from Washington to Paris or Paris to Washington to do their research, because those libraries have different purposes and the different purposes leads them to collect different stuff. That means one is not a better version of the other. They are not interchangeable at all.
On a local scale that's true as well. Most large universities have one big library that is the sort of repository for "stuff that doesn't go anywhere else." That's Google.
But they also have the law library, the engineering library, the theology library, the medical library. The reason I would schlep up the hill in Berkeley to go to the GTU to work is not because they had the same books in a different order and arrangement, but because they collected different books with a different purpose. It wasn't better or different for the sake of being different or because the cataloging principles were different. It was different for the sake of serving a different audience and fulfilling a different purpose.
All that to say that the way to break Google's stranglehold seems to me not to be not a search engine that indexes the same stuff with a different set of values or a different algorithm, but to index different stuff with a different purpose for a different audience.
Again, I hope this isn't rude, but every time I try an alternative search engine, including every time I've done blind side-by-side search, what I find is that the more niche I get, the more down in the weeds I get, the worse they all perform relative to Google. Google already does general search, but there are some types of search that Google does poorly. I don't really need someone to be better at general search. I need a search engine that is really good at searching for sixteenth-century history, a search engine that is really good at Middle French, a search engine that is really good at searching for natural history topics, and so on.
Some of those sort of exist (the Dictionnaire du Moyen Francais is incredible) and in those cases, I leave the Google-verse because what's offered elsewhere is not just better, but it lets me do things that are actually impossible on Google. If I have a question about a Middle French word, I'm not starting with Google. But cases like that are few and far between.
Bing tries to win by having a really nice home page and a very nice image search and essentially indexing all the same pages as Google. Duck Duck Go tries to win by pushing privacy, but not even having its own cralwers (that's still true isn't it?) and so it truly is just an alternative interface, without noteworthy differences in the way pages are indexed. Mojeek has its own crawlers and algos (right??), but again, when I've gotten at all niche with Mojeek, the results have been disappointing. So basically, they are all general search engines for the whole web that are trying to catch up with Google, but Google has this massive lead in indexing the general web.
The French people already built the Bibliotheque Nationale and it's here and Paris and I'm in Paris (not actually, but just for the purposes of argument). So why do I go to the library that is trying to collect all the same books as the BN, but will never actually catch up with as rich a general collection, but does have nicer chairs and faster internet? To me, that's Bing. It doesn't mean that my library shouldn't have books on French history and literature, but if that's their focus, nobody is going to come from Paris to wherever I am to use my library.
There are exceptions to that last comment. People do come from France to study French history topics at small institutes in the US because they have really focused collections that allow for efficient research and the efficiency gain is enough that they will, in fact, take a plane from Paris to use materials that, given enough time and energy, they can find in Paris.
The problem, of course, is that any niche that is commercial and takes away any noticeable share of Google, is going to get bought and put out of business by Google or possibly Microsoft. That's a unique problem and only anti-trust action can stop that from continuing.