it basically claims that since AI generated images are hard to predict there is not a strong enough chain between the prompt and the result that shows you have enough of an influence over the generated image. And that generating lots of images until one matches what you envisioned is also not good enough, like how searching the internet for an image that matches what you envisioned does not give you copyright over it.

Interesting, isn't this a direct consequence of knowing the general procedure a generative AI follows but not the individual steps it takes or works it leverages? If there was proper sourcing at every step you could actually have control and finesse on the output. But because the specific actions aren't documented, you're unable to move the algorithm in a specific enough direction to claim ownership.