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. Providing additional prompts does not change this, just as rerolling the dice wouldn't make the dice the author.

For that matter, gives extensive prompts or other artistic direction to a human artist would not make you eligible for copyright, either. Even if the artist was heavily influenced by your suggestions.

Finally, choosing one among many completed works is not a creative process, even if it requires artistic judgment. Choosing repeatedly does not transform it into a creative process. That's why choosing your favorite song does not mean you are a song creator.