Some of the reasons you might want to study the life of a famous composer i.e. Mozart, are to learn more about the story behind their music, information about their life that no one has discovered yet, or other mysterious things about the composer that no one knows about.
Because when you study the life of important artists, you learn about their techniques, their struggles to become good, their insights, their moments of sadness that were crucial to shaping their art. It will serve as an inspiration, and a guide to be as good as you can. In the case of a composer, when you look at the life of someone such as Beethoven or Mozart, you can see their efforts to become what they were. How the deafness of Beethoven aid him to be the composer he was (and to create the masterpieces he did)? Or the premature death of Mozart (he died at the age of 31), and how this was crucial to his compositions?
