For the very same reasons people read and write spoken language.
Modern society is built on the written word. This is why education focuses so much on literacy – reading ability is the best predictor for a successful life.
Deaf people don't have books that can teach them to read spoken language. Why? Because no writing system has existed for those books to be written in.
Literacy in a second language is much easier to learn when you are already literate in your own native language. This is one reason why sign language should be written.
Written sign language also enables Deaf poets, playwrights, and story tellers to record their culture as literature.