That's trying to apply two completely separate legal frameworks, with different purposes, and force them to come to the same conclusion about one aspect of each of them. It's not that simple.
It's perfectly legally consistent to say that AI-generated content has no copyright (because it's the product of a computer, not a human), and also that the human or organization operating an AI is legally responsible for anything in its output that is legally actionable.
Someone needs to hold legal responsibility for any piece of content out there. You can't just wrap your decisions in AI and get to be free of all liability for it.
But copyright isn't like that. There's nothing lost to society by saying that content is not copyrightable, and particularly given how the major LLMs were trained, there's a lot lost to society by saying that they can take all of that from everyone without consent, and then everything it produces has copyright and can be used for, say, Google's profit in perpetuity.