I think he was a good opportunity to set up Jon for his arrival on the wall. He saw his uncle as an honorable man, someone he looked up to and thought that most men who belonged to the Night's Watch were like his uncle. He was naive in that way like all the Stark kids seem to start out as naive children, which they all essentially are at least in the books.
Benjen served to build up the strong contrast to how the Night's Watch really is and served to set up Jon's first big conflict with having to deal with the real world so in that regard he is a fairly important character if only for a short time.