I can imagine of world of horrible patent trolls who have AI generating "art" constantly just so they can claim the work for themselves when a human artist creates something similar.
Thinking much further into the future: what will be really freaky is when society decides that only the AI has the right to copyright the AI's work.
You can do the same thing without AI.
For example: You can create all possible combinations of colored pixels in a grid of 800X600 with trivial code. Then you can publish all those combinations into a GitHub repo and now you own practically all art possible in a 800x600 grid.
As a bonus: you're now infringing the copyright of everyone who has ever created an 800x600 bitmap image.
Copyright is just incompatible with technology.
Of course, this ends up being a matter of likelihood. And if you generate all those combinations, but happen to select one in particular that is just like a pre-existing picture, the courts won't believe that was by accident. But the collection itself probably won't be infringing.