Considering Shakespeare wrote mostly blank verse (unrhymed) and Homer wrote unrhymed dactylic hexameter... I'd take that wager.
Greek and Latin poetry is actually almost never end-rhymed... because Greek and Latin are heavily inflected with lots of conjugations and declensions, the "endings" of words are often the same and a bit too obvious.
Rhyming poetry actually came into style for a couple centuries in English poetry... it's by no means a universal feature of poetry.
Edit: Also, I guarantee that "finding a rhyme" is not the bottleneck that's keeping modern poets from writing rhyming poetry.