Sorry - My fault for coining that phrase so I withdraw 'poetry illiterates' and use the term 'pedant' (to describe myself anyway) :-)

I think we are just using the word 'rhyme' in different contexts. My understanding of rhyme is the same as in the definition provided to Google by Oxford Languages. IE -

noun: rhyme

    correspondence of sound between words or the endings of words, especially when these are used at the ends of lines of poetry.
    "poetic features such as rhythm, rhyme, and alliteration"

Your definition seems to encompass what Oford Languages are calling 'poetic features'. Note that in the above definition they differentiate between rhyme and alliteration.

I do not accept that consonance, assonance and alliteration are the same as rhymes but I agree that they are poetic features. The song in question therefore, to me, contains no rhymes but does contain all the poetic features that you mention.

It is an academic pomt and matters not one jot to the enjoyment of the words so I think we just need to agree to differ on that one :-D