Song has been divorced from poetry for a long time, at least in the English-speaking world. I think that is to the impoverishment of poetry. There is the Shakespeare of dramatic blank verse, for instance, and the Shakespeare of the sonnets, but there is also the Shakespeare of the songs – and it is the songs that perhaps influence literature as much as anything else – lyrics made to be sung, but which we perceive now as words on a page. Songs and poetry were once indistinguishable (Sappho famously is supposed to have invented the Mixolydian mode), and have continued to feed one another: A. E. Housman, for instance, claimed that his influences were the Scottish Border Ballads (folk songs), the songs of Shakespeare and the poet Heinrich Heine (whose poems were themselves often set to music).
I’ve made a similar argument before, regarding rap lyrics and poetry: