So much in the space of folk (of many cultures), your examples are closer to that than most other music. Indeed some of the best music out there melds the poetry perfectly with the music. It's an art that doesn't exist if either part is missing.
The wing and the wheel they carry things away
Whether it's me that does the leavin' or the love that flies away
The moon outside my window looks so lonely tonight
Oh, there's a chunk out of it's middle big enough for an old fool to hide
Where are all the dreamers that I used know?
We used to linger beneath street lamps in the halos and the smoke
The wing and the wheel came to carry them away
Now they all live out in the suburbs where their dreams
Are in their children at play
There's a pale sky in the east all the stars are in the west
Oh, here's to all the dreamers may our open hearts find rest
The wing and the wheel are gonna carry us along
And we'll have memories for company long after the songs are gone
This is a good example of the technical restrictions that make lyrics a (proper) subset of poetry: note in particular the abundance of long vowels, which make it not just readable but singable.
Example that comes to mind, Nanci Griffith's 'Wing and the Wheel' - https://www.youtube.com/watch?v=FDs1kXTS9r8