Does a narratvie poem have to rhyme?
Not necessarily. But if a poem hopes to be recited and/or remembered, some such device as a strong meter and/or rhyming helps. A lot. Of course it’s a lot harder to write metrical or rhymed verse that makes good sense and doesn’t sound horrible than it is to arrange the usual rambling paragraphs of image-laden prose into “lines” on a page to look like poetry. But it’s worth the effort.
