So who is this person that knows so much about the Man-Moth? The voice speaks to us like the narrator of a National Geographic documentary. She has all the information, but she, herself, is not part of the story at all. (And we're just assuming it's a "she," since the poem doesn't clue us in otherwise.) More than that, she is an omniscient narrator because she knows what the man is thinking and doing, and she knows that the Man-Moth has fallen every time he's tried to climb to the moon and that he will continue to try (and fail).
She also knows what will happen if you catch the Man-Moth, though no one has actually done this in the poem.
This omniscient narrator/speaker, then, is important for this poem because we really need a birds-eye view to understand everything that's going on. If the speaker were the man on the street, there wouldn't be a poem at all because he isn't paying any attention. The Man-Moth doesn't sound like the type of guy to talk about himself much, so he'd probably make a pretty dull speaker himself (and who wants to hear someone yammer on about themselves anyway, right?). The only way to really get the whole story about the Man-Moth is to zoom out and get the story from someone who knows the whole picture.
Most importantly, the speaker does not judge. She allows us to draw our own conclusions about the Man-Moth and the people around him. It's important that she doesn't judge the Man-Moth because, ultimately, she's asking us not to judge him either—at least not on the thing that is outwardly apparent: that he's a little odd. She wants you to withhold judgment until you can hold that tear in your hand yourself and fully understand what the Man-Moth is about.