The intent of [US] copyright law is to promote new works of art (which can be derivative). So copyright did exactly what it is supposed to do in your analogy. Plus, you're human, which gives you special rights that software doesn't posses.
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.
If you take away enough of that effort, the investment in new stuff becomes unviable, perhaps.
Though this seems different issue from copywrite .
Like, we see that this can impact society, so we need some new laws to guard this.
Yes, because you're A) human and B) that is how copyright is supposed to work.
AI doesn't enjoy the rights of people. AI is a "talking book" and copying, storing, then repeating someone else's work from your talking book would (likely) run afoul of [US] copyright law.