Not only is paraphrasing important in the analysis of poetry, it IS how we analyze poetry. The prose and phrasing of poems simply do not lend themselves to conversational analysis and must be paraphrased to allow for a closer look at the meaning.
Paraphrasing is a dual test of a poem. First, an analysis needs the paraphrasing to properly examine the content in conversational tone. Secondly, it is important because paraphrasing allows the reader to test their understanding of the poem. For example, if lines or stanzas of the poem do not make sense when paraphrased, then either it's a really bad poem or more likely the reader has misinterpreted the intended meaning.
If a poem can withstand both tests, then it can be compared in standard language and compared against other poetry. A final consideration is translation. Foreign or older works can be tested for translation issues when paraphrased. There are some words and sentence structure which does not easily translate and could distort the message of the poem. Thus, paraphrasing can help ensure the complete meaning, if not the actual words, is properly transcribed.
Paraphrasing is an important part of analyzing a poem because it is a way for us to interpret a poem in our own words and make sense to it. When we paraphrase a poem, we take a deeper look at it and make it relevant to our own world. It helps us understand the context of the poem and look to find its ultimate message. It can also help us explain the poem to others who may find difficulty in understanding it. Through paraphrasing a poem, we can analyze the author's message, tone, and the main ideas.