It's still to be determined but I think the user should have copyright. After all, Photoshop already has automatic tools and nobody claims that the user loses copyright for using such tools.

In a finished AI image generator software, I expect there to be interractive functions. After you generate the first image, you can ask the AI to do stuff like "make the head funnier", or "keep the characters, but change the background". Then, the creative part very much involves the user as well as the AI.