As someone who reads poetry regularly and has played around a bit with AI-generated poems, AI poems can be quite impressive, but have a certain blandness to them. I can see them conforming very well to the average person's concept of what a poem is, whereas the human written poems might be less pleasingly perfect and average, more stylistically and structurally experimental etc. The LLM version is less likely to play with the rules and expectations for the medium, and more likely to produce something average and "correct", which makes some intuitive sense given the way it works.
I think when asked to rate poetry as human or ai authored that human poetry does look more like a random smattering of semi-related words which, I assume, is what folks think machine generated poetry would look like.
Perfect grammar and perfect meter doesn't read as AI to most folks yet.
LLM’s also have no life experience, so they can wrote poems, but those poems aren’t communicating anything real. Poetry in the vein of Whitman and Dickinson and Plath is very much about a person expressing their very personal experiences and emotions.
