But you can't stop people from sitting and studying your painting and then painting stuff similar to it.
One of the core assertions that is being decided in this case is if there is any actual reproduction here. Does a model contain a reproduction of every image it was trained on? Can the model actually create a reproduction of any images it was trained on?
If it turns out that there is no reproduction here, then it comes down to how much legal control we give copyright owners to regulate access.
A gallery can reasonably ban cameras and canvases, but it becomes a lot less reasonable if they try to ban artists.
Let's imagine that this isn't just specifically tuned ML but proper General AI that can learn new skills. Is your argument that this AI would be legally prohibited from viewing any images it doesn't have a specific license for?
I think that drawing hard lines around what kind of processing can be done on publicly available images is going to become problematic. It's better to regulate around what can be done with the results of the processing than that processing itself. That's how our existing laws work. Making a reproduction, even just from memory, of a copyrighted work is restricted. Memorizing a copyrighted work is not.