Rhyme Can Be More Heartfelt
I have written poems for people but never publicly. The case for writing a poem usually relies on how deliberate it is compare to an essay. Simply writing can always have a pinch of free flow to it that is far more liberating save for grammatical and social conventions. Poems on the other hand tend to have rules, rules that readers should be able to understand.
I've only ever attempted writing one poem with no rhyme. I hated it. This isn't to say they're bad. Rhymes make poem rules easier because the instructions are simple. A less understood part of rhyming would be the rhythm in a poem, otherwise the rhymes won't work.
I can respect a non-rhyming poem which can masterfully convey its rules to the reader. A poem that does this well tends to make for better art... in my humble opinion.