The second is that there are only five Japanese vowels and each one creates a single syllable nucleus, so every character rhymes with 20% of every other character, so there's no real skill, and hence, no real point in rhyming? (Whereas English has far more syllable nuclei and words can vary between one to many, many syllables, so certain words are quite hard to rhyme)

There are two aspects to meter; the placement of stressed syllables and the placement of syllables of different lengths itself. Actually English as opposed to Greek and Romance languages that are not French has stress patterns that are highly dependent on the phrase rather than on syllable position in words, and so traditional forms are felt to be quite artificial in English, and perhaps this encouraged the development of free meter in modern English poetry.

Anyway, the stress aspect of meter I don't think features greatly in Japanese poetry. On the other hand, meter still features prominently in Japanese standard poetic forms; are characterized as having a set number of syllables in each line, but renku looks instead at the number of morae (short syllables have one; long have two).

So do Italian words, but we still have plenty of rhymes. From my almost non-existing Japanese knowledge, I don't really get what you mean.

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.

Several times over the years I've had the "hey, were you aware that virtually every English song rhymes from start to finish?" conversation with a number of native JP speakers, and in every case so far they were very surprised. And even when the person is quite fluent in English, although they get the concept intellectually they always have a lot of trouble discerning the rhymes unaided.

Rakim (of Eric B. & Rakim) was one of the first to take this to new heights.

An example from "Lyrics of Fury", with the rhyming words emphasized in caps:

    The SCENE of the CRIME every NIGHT at the SHOW 

    The FIEND of the RHYME on the MIC that you KNOW