In general, poetry is a great component to any language learning (enhanced by the fact they're often published in dual language version), but it's essential for dead languages.
Poetry is actually much worse for learning a language than prose is, because the language used in poetry is usually not typical and not uncommonly fairly strained. Any advantage of poetry comes from how much the student enjoys it.
> but it's essential for dead languages.
Why would dead languages be any different in this regard from living ones?
As to poetry in general: Poetic language is challenging, diverse in vocabulary, and because of meter it is memorizable, which I find puts more of the language "in my head". Poetry is also an essential part of most national literatures, and so a big component of really learning a language beyond being conversational.
Nothing in my answer disparaged prose, or that poetry is more important than prose; any language learning consists of repeated, effortful exposure to many language sources, as well as speaking and writing the language. I'm just emphasizing that studying poems in other languages can really help learning those languages, so a savvy student should include it. The tone of your response is puzzling to me.
This is a matter of taste.
> I have never had a conversation in any dead language.
This is also a matter of taste.
> Prose literature is actually a more recent development, so if you want to read ancient stories in the original, which are awesome, you will be reading poetry.
This is more of a matter of which language you're studying.
> because of meter [poetic language] is memorizable
This is bizarre. Your claim is quite correct as to speakers of the original language, but we've stipulated that the language is dead. In general, students cannot identify or even notice poetic meter in the dead languages they study. I really enjoyed scanning Latin verse, but that is because I enjoy math. To more "normal" students, scansion is infamous for being painful and difficult.
I responded to the perceived suggestion that studying poetry is an effective method of learning a language. I don't agree with that: poetry is more difficult to read than prose, and the lessons you may draw from it are often specific to the genre, not the language. For example, if you want to read Latin poetry, you will want a working knowledge of Greek grammar, which is sometimes used in preference to Latin grammar. The Roman poets could count on their audience to know Greek. But learning Greek grammar is not actually a particularly valuable step in studying Latin grammar.
You don't read poetry in order to learn a language. You learn the language in order to read the poetry.