Rights to virtual live shows are major stakes here.
Fans creating their own songs should just whet appetite to see live shows, which is where the money is shifting anyway. But live productions creating exciting virtual performances without input or permission from the artist threatens the live show revenue.
One potential threat from fan-generated music we haven't dealt with yet is a popular fake diverging too much from what the actual artist does. If the artist won't accommodate this, it would create an opportunity for a similar artist to perform the music. It'd be like when an artist's popular song is one they hate, and they have to decide whether to give people what they want.