The US copyright office has published a statement that they see AI output analogous to a human contracting the work out to a machine. The machine would hold the copyright, but can't, consequently there is none. Which is imho slightly surprising since your argument about choice of prompt and output seems analogous to the argument that lead to photographs being subject to copyright despite being made by a machine.

On the other hand in a way the opinion of the US copyright office doesn't matter, what matters is what the courts decide