And arguably, neither the image generator did. Who did were the artists

In which case, neither the image generator nor its operator are eligible for copyright.

The same reasoning still applies to Stable Diffusion etc., given that you can heavily tweak the output through your prompt.

The point is that the AI generator (or, if you prefer, its training data) exercised direct control over the image, not you. For that matter, giving extensive prompts or other iterated artistic direction to a human artist would not make you eligible for copyright, either. Even if the artist was heavily influenced by your suggestions. There is a fundamental difference between an art creator and an art critic.

Finally, choosing one among many completed works is not a creative process, even if it requires artistic judgment. That’s why choosing your favorite song does not in any way make you a song creator. Even if you know that all the songs you don’t choose will be destroyed.