One could literally take Claude 3.5 Sonnet New or o1-preview and disprove this in an hour or two just by prompting the AI to try to exhibit the type of poetry you want and then maybe asking it to do a little bit of automated critique and refinement.
You can also experiment with having a higher temperature, (maybe just for the first draft).
You claim that LLMs can't make poetry like that. I bet they can if you just ask them to.
They could, but they probably won't. Poems like GP are basically using the power of emotional manipulation for good, and companies like Anthropic try very hard to prevent Claude from having that capability.
What he said was basically that it just couldn't create unexpected verses or break form. Since supposedly it can only do the most probable token -- but that's not how sampling works unless you use temperature 0. And it can easily be instructed to break from a strict form (which would create a new variation of the form) for effect if it made sense.
You could also ask it to create a new form and it could. I don't work for you so I don't have to create examples, but anyone who has used the latest SOTA models for any amount of time knows this capability is expected, and if you were really interested then you would try it. If you feel the result isn't very good, ask it to improve it.
I could program even a markov chain to generate a lot of odd unusual potentially interesting stuff, but no one would call any of it a new form of poetry, because establishing something like that requires social status, which robots don't have.
You can also experiment with having a higher temperature, (maybe just for the first draft).
You claim that LLMs can't make poetry like that. I bet they can if you just ask them to.