Two people could generate the same short story through different creative processes too.

That doesn’t work with AI for a variety of technical and practical reasons.

As a rule, the law doesn't care about technicalities or practicalities.

Two people could, completely coincidentally, generate something that is so similar that it looks the same at a glance… even with dramatically different prompts on dramatically different models.

Sure. If two humans take a photo of the same sunset standing next to each other, they will be virtually identical and they will both own full copyright protection for the photo they took.

That protection does make the other person's photo an illegal copy - because it wasn't a copy.

No, the output of an AI is fundamentally “coincidental” and should not be subject to copyright. Human intent and authorship MUST be a significant factor. An artist can still use AI in their workflow, but their direct involvement and manipulation must be meaningfully “transformative” for copyright to apply in a fair and equitable way.

Of course. By the way that applies to human created works too. Copyright doesn't apply to everything created by a human, only certain things are protected. If someone asks you what 2 plus 2 is, and you reply "4"... you don't own the copyright on that answer. It wasn't creative enough to be protected under copyright. If you reply with a funny joke, then that's protected.

No, the output of an AI is fundamentally “coincidental” and should not be subject to copyright.

If the image generator in question generated a piece of content that looks similar enough to some piece of content protected by copyright, odds are that it has been trained with it, or that both were produced with the same set of pieces of content.

That shows that the issue might be elsewhere - it isn't the output of the image generators, but the works being fed into the generator, when "training" them. (IMO the word "training" is rather misleading here.)

Human intent and authorship MUST be a significant factor.

Refer to the link in the OP, regarding photography. All this discussion about "intent" (whatever this means) and authorship has been already addressed by legal systems, a long time ago.

their direct involvement and manipulation must be meaningfully “transformative” for copyright to apply in a fair and equitable way.

What does "meaningfully" mean in this context? It's common for people using Stable Diffusion and similar models to create a bunch of images and trash most of them away; or to pick the output and "fix" it by hand. I'd argue that both are already meaningful enough.

If anything, this only highlights how the copyright laws were already broken, even before image gen...