Scale matters, and the scale that computers/these AIs operate under are absurd compared to a person doing it manually.
The work of a person can be mitigated and a person can be held accountable for their actions.
Much of our society operates on the idea that we don’t need to codify and enforce every single good or bad thing due to these reasons; and having such an underpinning affords us greater personal freedom.
I believe that this kind of generative AI is bad because it approximates human behavior at an inhuman scale and cannot be held accountable in any way. This upends the entire social structure upon which humans have relied to keep each other in-check since the advent of the modern concept of "justice" beginning with the Code of Hammurabi.
In essence: Because you cannot punish, rehabilitate or extract recompense from a machine, it should not be allowed in any way to approximate a member of society.
This logic does not apply to machines that "automate" labor, because those machines do not approximate human communication - they do not pretend to be us.
Should those machines then be subject to your same philosophies? I'd suspect you'd say "that's different" somehow but it is only because you are alive at this moment and these machines have been normalized to you that you do not care about them. Were you to be born in a few centuries, you would likely feel the same way most do about the prior machines, and indeed, you'd be hard pressed to find anyone who think that future generation's AI (probably simply called technology then) is problematic as you do today. Recency bias is one hell of a drug.
Even then, their work as output can matter but that doesn't necessarily mean they (should) have a per se right to their work without other people also using it, especially in cases where their work is not used as outputs directly, which is what plagiarism is. If that were the case, no one could learn from a other's work, regardless of whether that one is a person or a computer.
I don't think there is a way to continue this particular branch of this argument without devolving into a debate on the value of human life like a couple of Macedonian philosophers - suffice to say, my point of view is that the work of others has intrinsic value tied to intent, and machines do not have intent.
If no output of humans has intrinsic value, then once machines can approximate humans sufficiently there is no reason for humans to exist - and that is an outcome that I, as a human, reject with all of my being.
The reason for humans existing is not because of the output they produce (indeed, that is dystopic), humans have worth inherently, regardless of what they output. This is also what nihilists have figured out, so maybe that is something you should look into if you seriously have such an opinion as expressed in your last paragraph.
[0] https://news.ycombinator.com/item?id=40919253&p=2#40920318