One of the things that distinguishes poetry from ordinary speech is that in a very few number of words, poetry captures some kind of deep feeling, and rhythm is the way to get there. Rhythm is the way the poetry carries itself.
Rhythm is sound in motion. It is related to the pulse, the heartbeat, the way we breathe. It rises and falls. It takes us into ourselves; it takes us out of ourselves.
When poetry separates from song, then the words have to carry all the rhythm themselves; they have to do all the work. They can't rely on the singing voice.