Even leaving aside that some people think coming up a prompt or choosing from multiple generated images is itself work enough to justify copyright you'll have so many very similar images registered that copyright trolls could still intimidate people into forking over settlement money and people would still argue that even the smallest changes (say to brightness level/saturation) justifies their copyright.
Leaving AI generated works free from copyright would be ideal, since it'd free those images for others to build off of and remix and reuse in new ways, it encourages commercial projects to hire human artists so that they can gain the protection of copyright, and it doesn't stop anyone from doing what they want with the technology. Comic book authors who illustrate their work using AI can still copyright their stories, trademark their characters, etc.