It shows you are not a lawyer. You misunderstand how copyright works. Creating copies or derivative works and distributing those is all that matters under copyright. This is not "disregarding" copyright (which is not an actual thing) but something that is either fair use or may require some kind of permission from the creators of the original by those distributing some kind of derived work or copy. That's why it's called copyright.

Copyright merely restricts the distribution of original works or their derivatives. In case of an infringement, copyright holders can insist you stop distribution and/or compensate them for that.

If I sell you a paint brush, I'm not liable for you putting a red nose on the mona lisa and trying to sell it off as an original work. Doing that on the original would be an act of vandalism (because you don't own it) and doing that on a replica that you got from somewhere infringes on the rights of those that created the replica. Which is a derived work or copy in itself of course and the distribution of that is regulated by copyright. Distribution of such a replica is of course fine because Da Vinci has been dead for a very long time and his work would no longer be protected under copyright. Distributing your red nosed mona lisa would therefore be fine too. Either way, the paint brush seller is no party in this case this is between you, Da Vinci, his descendants, and the replica creators.

Now your assertions as to what AIs are of aren't, are simply not relevant. You assert it's a statistics algorithms thingy. That sounds like a tool to me. Yet another paint brush. Using a paint brush is not infringing on anyone's rights. For that you have to distribute the results of your work. The nature of the tool does not matter. How you use the tool does not matter either. You merely create (potentially) derivative works with the tool and what you do with those matters. Especially when you distribute them to others. One of those derivative works is of course the AI model itself. Creating one is fine. Copyright gets potentially infringed when you distribute one.

Now we get to the core of the matter. Can you with a straight face say the AI model resembles the original and is a derivative work. It doesn't actually look like or resemble the original in any shape or form. Even proving the AI model is derived from the original is tricky. Copyright is not about protecting vague ideas or notions but the concrete shape or form of things. And it's only an infringement if you distribute a derived work or a copy of a thing to others. So, merely creating an AI model is not distributing anything to anyone. You are merely using tools to create something for yourself. An AI model in this case.

Distributing a verbatim copy of a book is an infringement. Citing the book in your own work is fair use (up to a point). Paraphrasing elements from the book, acknowledging it exists, taking inspiration of it, or reading it aren't copyright infringements.

The legal problem with AI models is that their concrete shape or form doesn't resemble the original inputs in any shape or form. Besides, companies like OpenAI don't actually distribute their AI models. They are huge; it's not very practical. They merely exploit those models to generate outputs to inputs from their users and customers. Are those outputs derivative works? Maybe, but that's where it gets tricky. They clearly aren't in the classical sense. Not even close. But if you somehow could conclude that they are, who is distributing that derivative work? Secondly, it the AI model is a tool, who actually creates those outputs and are those outputs protected under copyright? Who actually holds those rights? And how would you tell apart such an output from a human created one?

It's questions like this that make all this extremely murky from a legal point of view. IMHO without dramatic changes to copyright law or the way it has been commonly interpreted legally, it's just very poorly suited to do anything about stopping AI companies from doing what they are doing. You'd have to bend the conventional interpretation quite a bit for that. No doubt, there will be court cases where people will try to do that. But it will take many years before the dust settles on that. And I wouldn't get my hopes up on some unexpected/dramatic outcome.