I don't fundamentally disagree with you, but what you are saying doesn't hold water.
> a copy is made and reproduced numerous times when training.
Casually browsing the web creates millions of copies of what are likely the same images and text that models are trained on. Computers cannot move information, they can only copy it and delete the original. Splitting hairs over the semantics of what it means to "copy" isn't a strong argument.
> where it is an authorized viewing
What exactly is an unauthorized viewing of a publicly accessible piece of content online that has been hyperlinked to? If we assume things like robots.txt are respected, what makes the access of that data improper?
> it may output material that competes with the original
An art student could create a forgery. I could craft for myself a replica of a luxury bag. But that's not a crime unless it's done with the intention of deceiving someone or profiting from the work. Intent, after all, is nine tenths of the law.
It's an important right that you should be able to do and create things, even if the sale or distribution of the outputs of those things are prohibited. The ability for a model to produce content which couldn't be distributed shouldn't preempt its existence.
> So you may have copyright violation in distribution of the dataset or a model's output
And neither of those things are the act of training or distributing the model itself!