Instead, I feel like the objections are (rightly) these two issues:
1. GenAI operates at a much larger scale than an individual artist. I don't think artists would have an issue with someone commissioning a portrait say in the style Van Gogh (copyright argument). They would have an issue if that artist painted 100,000 pictures a day in the style of Van Gogh.
2. Lack of giving back: some of the greatest artists have internalized great art from previous generations, and then something miraculous happens. An entirely new style emerges. They have now given back to the community that incubated them. I don't really see this same giving back with GenAI.
Edit: one other thought. Adobe used their own legally created art to train their model, and people still complain about it, so I don't buy the copyright argument if they're upset about Adobe's GenAI.
Edit 2: I'm not condoning blatant copyright infringement like is detailed in this post.