Nobody (to my knowledge) has ever said that you can't train on copyrighted material - what you aren't allowed to do is copy or directly plagiarize. Something that all the generative systems are going to great pains to remove from their system where possible.
Are they doing a perfect job - nope. But they'll get better, and this is good - copyrights are supposed to prevent replication, not use of their material.
Also, performance licenses for movies, plays, recorded music, and copyrighted scores are all required. The lack of copying is not relevant there, the performance alone can be infringing.
I like that you bring up music - almost every musician you have ever listened to (some exceptions of course) developed their talent by learning from others - chords, bridges, etc... And I'm just as certain that close to 0% of them had a "license to learn" from their material.
I lost all optimism with tech hoping "they'll get better" quite a while ago. No, it's time to regulate them before they burn the bridge this time.