Well OK, so what if I put my copyrighted prompt through the mechanical transformation process of the AI model?
... then all elements of the prompt that come from your human creativity and that survive into the final result remain under your copyright. Which in most cases should be almost as good as owning the full copyright, although it might influence fair use defenses if even a full copy infringes on only a minor portion of the work.
I think the point is to decide where to draw the line. An AI model is a stochastic process, you don't get the same results from the same prompt (even at temperature 0 because the GPU will do multiplications in a different order and errors compound). It's not really the same as a digital compositing pipeline and a lighting engine.
Also you have to account for the PB of training data which consists of copyrighted works that goes into the model and is interpolated to produce the result. Personally this tips the balance to AI output being new work that's not copyrightable for me because otherwise all of the people who own copyright on the training data should have joint copyright of the output too because in a sense all of the training data is part of the prompt too.
Your prompt doesn't really contain all of the decisions that were made in the final output most of the time. When you use a rendering engine it does contain only your decisions and you have a license to use the work of all the people who created the software and other assets you're using to make the film.