One example: this weekend I was looking for lyrics from the British folk band Why?. I know they exist; my brother has a bunch of their albums. I have quoted lyrics at Google, I've searched for it on Youtube, I've searched for the band name combined with song titles or names of band members, and I found tons other bands and other random crap, but not the band I was looking for. Eventually I searched for a very specific phrase that was also the title of one of their live albums: "Jig at a Why? Gig", and that finally turned up results.
It's an obscure band, and their name being a common word certainly doesn't help, but certainly combined with song titles, lyrics and band members, it should be pretty clear what I'm looking for? But with Google giving strong preference to the most popular results, Google becomes primarily good at finding things you don't need a search engine for to find them. I want a search engine that's good at finding things that are lost, rather than in plain sight.