I’ve said this before, but there are rhymes in songs like Dirty Old Town, America, etc, but they are not perfect clean rhymes. Assonance and consonance are rhyme types where the sound of the vowels or the sound of the consonants rhyme, even though the whole word does not. “Empty and aching and I don’t know why, counting the cars on the New Jersey Turnpike” “Dreamed a dream by the old canal, kissed my girl by the factory wall”. Sometimes the rhymes are internal, rather than at the end of lines, and sometimes are just repeated initial letters (alliteration) “in a deep and dark December”.

And the leaves that are green (assonance) turn to brown (consonance)
And they whither the wind (alliteration)
and they crumble in your hand (assonance).