The problem is that when you share a song, you’re sharing a link that isn’t tied to your account. That is, everyone who shares a song in the public library is sending the same URL, the same link. So there’s no way to grab your notes based on that link. I suppose I could add that association to the URL, but that adds more complexity too because now you have to make it clear that this is happening, and it makes the URLs longer, and what happens if someone saves the song to their own library?
Similarly, say you have a public song on a shared list. You couldn’t just make the notes visible to anyone who can see the song, because strangers wouldn’t want to see other people’s notes. So what do you do? Attach the notes to the list? Embed something in the link? How does that work with lists?
I’m only posing these questions a) to think out loud a bit, and b) to offer some details as to why it’s tricky to implement. The more I think about it, a “groups” feature might be the simplest way forward, in fact! But I haven’t thought this through entirely either, so I may be missing something.
The About field is meant more for transcription notes, song authorship notes, etc… it’s read-only for public songs and limited in length. I still wonder if this should have been combined with the Notepad… or even the References area as well… 
It is a very complex process to make something that ends up as simple as possible. 
I appreciate your thoughts and feedback!