The importance of the narrative aspect of Richard Rodriguez's essay "Aria: A Memoir of a Bilingual Childhood" lies in the fact that he is not offering a fictional perspective.
Rodriguez, in his essay, is providing the reader with a first hand account of what life was like for a student in the American schools whose native language was not English. Without this poignant perspective, many readers (both Spanish speaking and American speaking) would, most likely, fail to see the true impact of his story.
Many first-person narrations are essential to an author's desire to engage the reader, gain their sympathy (or empathy), and relate true facts to the reader. Without the first-person recollection, some readers may find the text to be fictitious.
Therefore, the narrative aspect of the essay provides readers with a true historical recollection of Rodriguez's life as a student in American schools fighting for the right to keep his family's language separate from that of the English language. It is necessary for the narrative to function in such a way that allows readers to understand Rodriguez's reasoning regarding keeping his family's language sacred.