Couldn't we have a music:// protocol or something, to be opened by the OS's preferred music app? Anything like that already exist?
You're probably right that it would end up being more clunky and broken.
But I think a song is much closer to a resource (like a hyperlink to a website), than to a contact address (like a mailto link).
This is actually a regular problem for me, and I solved it by backing up my messages, then using a script to scan them for music URLs, and create a playlist on my music service of choice. It felt like a pretty silly thing to create.
Spotify already use some of those, but I dunno if they expose via API or make it searchable.