If words in songs resonate with you, then surely they are rhyming, but on another level?

You could also argue that the best rhymes are the ones that pass you by unnoticed anyway (as those above in Leaves that Are Green), and like this (alliteration and assonance)::
I’m empty and aching and I don’t know why,
Counting the cars on the New Jersey Turnpike…
Again, don’t let’s be too hasty to complain about the absence of rhymes.

Too many perfect rhymes in a song can be rather distracting from the narrative, and even be a bit crass, hence the greater reliance on them in comedy songs for humorous effect. Dylan must have had great fun in log piling such rhymes in It’s All Right, Ma, All I Want to Do, Fourth Time Round, etc, etc.