Some of these lawsuits are trying to prevent the AI from even 'reading' the material. It can't even be used as an influence.
Wouldn't it be better to treat the products of the AI with the same laws as humans. If the new 'product' is 'too close' to something existing, then they get sued. Just like a musician that has a song with a few notes that sound a little too close to someone's song from 30 years ago gets sued. The songwriter was allowed to listen to the music, it went into their brain and became an influence. If that influence becomes too great, then it can be sued.