Here's a short essay on it I wrote a long time ago.

I would rewrite a lot of this now for general quality, but I think my thesis is sound:

https://albertstimson.wordpress.com/2015/01/23/why-poetry/

Of note: this takes a fairly strict definition of what poetry even is, and I would argue that a lot of things that superficially look like poems don't accomplish any of what makes a poem be worthwhile as something different from prose.