They all do. And let me elaborate on that.
For starters, there’s the element of formal craft in poetry, and there’s the allusive use of language in poetry. Both of them are essential.
For allusiveness, what you need is a culture expressed through that language. All natural languages that people live their lives in are vehicles for culture. Yes, some literature cultures will have a huge backlog of canon to allude to; but oral cultures are no slouches there either. The subtle allusions to layers of Roman mythology make Latin literature very dense, and difficult to get through for an outsider. But Roman mythology is not that far removed from the religion of any given preliterate tribe, and their oral literature will not be any less powerfully allusive for it.
The languages that are in a disadvantage there are constructed languages. Esperanto is not at a severe disadvantage, since much of its literature for the most part is still squarely in the European tradition, and there are both internal and external allusions it still makes. But compared to ethnic languages, it’s fair to say, Esperanto is a bit more of a blunt instrument.
Klingon’s even blunter, though at least Klingon has a mythos. I still have a soft spot for the Klingon terza rima I came up with though…
Then there’s the formal element of poetry. I have to say, talk of which languages it’s easier to rhyme in is cheap. The forms adjust to accomodate the possibilities of the language. If rhymes are easy, you have rhyme-rich forms like the Petrarchan sonnet. If rhymes are less thickly strewn on the ground, you dial that back to the Spenserian or the Shakespearean sonnet. If rhymes are hard, you’ll allow all sorts of off-rhymes; if rhymes are facile, you’ll frown on suffix rhymes, and put hurdles in the way like Rime riche. The resources of the language are so harnessed in the language, that the exercise of craft is enough of a challenge to be appreciated, and not so much of a challenge as to be impossible.
Not all poetic traditions use rhyme, but many poetic traditions do something like that. (I’d like to think all do.) In Latin poetry, having the ictus coincide with the metre (stress coinciding with the feet of quantitative metre) was gauche, tolerable only in the very first poets in the language like Ennius.
So, I could say that Italian is a rhyme-rich, clear-sounding, culturally fertile language, well suited for Petrarch. And English is rhyme-poor, muffled, and came into the 17th century blinking and deracinated. So Early Modern Italian must be better suited for poetry than Early Modern English, right?