Realistically this is less of an issue than people make out...
The Mona Lisa is out of Copyright. If I take a photo of the Mona Lisa, I hold the Copyright on that photo. The barrier for something to be copyrightable is very low. Even picking your favourite AI generated image from a choice of 5 probably is enough for there to be "human creativity" of some kind.
Interestingly, this is the problem that the website that "generated every possible sequence of musical notes" ran into. No creativity, so no copyright ownership...
In any case, until an AI produces Mickey Mouse, there probably won't be issues. Copyright is often an "in hindsight" legal question.