It is a bit more complicated than that, and the legal motivation from the Copyright Office is different than what you describe.
One of the most informative cases, in my opinion, is the Copyright Office's back and forth on Zarya of the Dawn. In their view, even thousands of refining prompts cannot be sufficient to convey copyright protection on an AI generated image since it lacks the necessary control and connection to the person. Suryast is another helpful case. I think they're still very incomplete when you start to consider works like those from Jackson Pollock or, my personal favorite hypo, an artist with a prosthetic that uses statistical machine learning to control the end effector and thus the paintbrush. But those are just hypotheticals for now.
I help chair a conference of IP attorneys and others who specialize in software licensing and AI so we've been talking about this for a while now. We actually just had the conference this week so I can probably share some resources or presentations if people really want to get nerdy about it.