I'm sorry, I didn't intend to make a case for Japanese not rhyming with what I mentioned. I intended to illustrate how rhyming looks like in Japanese, but rereading my comment it does indeed look like that.

I just wanted to establish that Japanese poems were characterized primarily by # of syllables or # of morae, and were quite free in their distribution of stressed syllables or long/short (heavy/light) syllables, as opposed to most European forms.

I'd also like to address a misconception of the original comment I was responding to that rhyming in poetry is prevalent in a language because it takes skill. It's primarily a matter of poetic tradition whether a language's poetry cares about rhyme. As darkwater's comment points out, Italian has plenty of rhymes and its poetic forms use rhyming extensively.