The value add of Genius isnt so much in the lyrics but in the explanation and context given grom Genius. I have even seen actual artists confirm interpretations and explain some things as well I think Hittman from Dr. Dre's 2001 album was one such artist if I remember correctly.
I do see what you are saying on the other hand but I dont think that lyrics written down from a song are some random websites copyright / property.
"Ownership" such as it is for intellectual property is still with the copyright holder(s), which is why it makes sense that you don't have the same rights you would if it were truly "your" song.
As a listener, you either own a physical product that happens to have been made with those licenses, or you're listening to a performance, if you're streaming. Neither of these things give you further rights with the song or recording.
This stuff is pretty wacky, and I may have some of those details wrong. I took a class in music industry law a decade ago
Why? It's pretty much a poem.
The ones printed in the booklet that came with the CD or encoded in the mp3 file?
If Google is simply scraping that content from them without permission then that has been litigated many times in court and almost always comes out badly for the "scraper".
But if Google is not sending traffic to Genius and using Genius as the source for some of it's lyrics, that's shady as hell. That's anti-trust.
https://www.nytimes.com/2014/05/07/business/media/rap-genius...
I wonder how much they have to pay?