Hi, Sarah - I've moved this to the main Poetry forum; I don't know how it ended up in the Chapbook.
Is rhyme important? It's one of the devices available to poets, and there might be a number of reasons to use it. If it's the right tool for the job, then it's a good one to use. Otherwise, no. So it's up to the poet.
It can enhance a poem's lyrical qualities: while it's less common in poetry than it used to be, rhyming is still very much standard practice in songwriting. (For that matter, not rhyming has been prevalent in poetry for a long time now - let's say about a hundred years or so.)
I've read that one use for rhymes is as a mnemonic device: they help to remember the poem. This aspect would have been important when poems or stories weren't written, but shared verbally.
I think rhyme has a stigma attached to it today because people feel obliged to use it, and it's used poorly or inappropriately. It is (unfairly, I think) assumed often that rhyme makes poems juvenile or cliché.
Perhaps because of the mnemonic aspect and the compulsion to overuse rhyme, I think we end up with bad poems that are easy to remember. Bad poems that don't rhyme are more easily forgotten.
Rhyme is good, but it's not compulsory.