A lot of people misunderstand the purpose and implementation of copyright.
To make things even more confusing, most people only understand the US version of copyright. The US has worked really hard to get the rest if the world to align their copyright law with the US, but they’re all subtly, and sometimes not so subtly, different, even before you get to the different legal systems used to interpret and implement copyright law.
The first thing is: copyright is about the right of a human creator to control how a copy of their work is made available (publicly in some countries, any in others) for a limited time. In some places that right can be temporarily or permanently assigned or sold to someone else.
So when it comes to AI, one group argues that unless the rights holder licenses the work to be part of a training set, it’s not allowed to be part of a training set.
Another group says that it doesn’t matter; if the human creating the training set got the work legitimately, they can use it to train a model.
The models themselves do not contain any copyrighted material and so are outside the discussion.
Copyright is flexible; for music, we have different copyright rules for recording, reproducing, and performing music for personal or public consumption, with different copyright for music and lyrics and associated video.
This could also be applied to AI, with training models being a new “recipient” of copyrighted content. We could enshrine in law how this can be done legally. But so far, we haven’t, so it falls back to “is this fair use?” and “are different copyright permissions needed when a human is not consuming the work?”
The end bit, that AI created works aren’t copyrightable, is already settled. However, any work a human does to tweak or select AI generated content, if it is itself creative, is copyrightable.
So yes, copyright should exist. People need to re-learn what it actually is though, and additions may be required to the laws in order to enable AI generated art to promote valuable skills and knowledge.