I always hated this. It's been historically hard to get easy access to lyrics of songs you've bought! It always made no sense to me that you couldn't publish lyrics of songs.
I think legally you likely have not "bought" a song, you have licensed it. The license includes the right to listen to the song, but not to redistribute either the music or the lyrics.
"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.
To add a little nuance to this, there are two copyrights at play here, the song and the recording. The songwriter (who may or may not be one of the performers) originally owns the rights to the song, but often sells them to a publishing company. The lyrics pertain to the song. The recording is made with a mechanical license to the rights of the song, and a CD is distributed with a license to the recording (owned by the band, unless they recorded as a work-for-hire for their their record label, which is typical).
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
Maybe in the context of streaming, but when you buy a CD, AFAIK, you own the copy, but there are limits on what you can do with it because of copyright laws; Just because I own something, doesn’t mean I can make a copy and give it away. That
