Japanese can only end in ‘a’, ‘i’, ‘u’, ‘e’, ‘o’, or ‘n’. Rhyming in Japanese is boring because it has so few possible endings that tons of stuff rhymes. Haiku, tanka, and other forms exist with syllable*, rhythm, and even thematic rules instead.

IIRC, Anglo-Saxon poetry before the Norman conquest also wasn’t into rhyming.

* it’s technically not syllables but close enough for this usage.