I don't think you actually need copyrighted data to train AI to compete with artists. The argument over copyright is interesting but kind of a sideshow. We already know that copyright protection is not a prerequisite for creativity - as it currently stands copyright only protects the rich.
The real reason why AI is going to kill DA/NG/SF/GH/etc is because of spam.
Let's say, for every piece a 100% human artist can do with no AI assistance, another artist using AI as a tool can make three. They start off with a prompt in DALL-E, SD, or Midjourney, and then tweak the output with prompts and so on to get exactly what they want quicker.
Now imagine a non-artist using the same technology. They don't care about the touchups. They just want to churn out lots of pieces all at once. So that would be nine times more output compared to the unassisted human - three times three. And there are plenty of them doing this, because they all watched the same video on how you can hustle T-shirt and poster stores by submitting lots of AI-generated pieces.
The reason why you are seeing art sites ban AI art is purely a matter of practicality. Many of those spaces are able to provide free promotion to people who post quality content because quality is itself a limited resource. Now the human trying to make their magnum opus - AI or no - is going to be buried under lots of low-effort garbage from zombie modernist grifters.