A major difference between a human training himself by looking at art, and a computer doing it, is that the human ends up working for himself, the computer is owned by some billionaire.
One enhances the creative potential of humanity as a whole, the other consolidates it in the hands of the already-powerful.
Another major difference is that a human can't use that knowledge to mass-produce that art at a scale that will put other artists in the poorhouse. The computer can.
Copyright exists to benefit humanity as a whole... And frankly, I see no reason for why a neural network's output should be protected by copyright. Only humans can produce copyrightable works, and a prompt is not a sufficient creative input.