It is easy for each blind man to jump to conclusions based on limited experience and first impressions. Saxe is telling his audience not to assume you have the whole truth just because you know one part of the truth. Don't rely on first impressions to tell you all you need to know. If we share our perspectives we will come to a more complete understanding of the truth. Working together is more effective than working alone.
Stories are more involving, creating images and pictures.
People can remember and identify with Saxe's message because of the form he chose to convey it.