The writing requirement exists because faculty believe in it. Graduation requirements are set by vote of the entire faculty of the College of Arts and Sciences, not by any single administrative office. Requirements are changed only after long study and public discussion among the faculty at large.
Faculty believe in writing requirements because they believe in students.
University teachers know from experience that writing is necessary to full participation in all the professions and in every scholarly discipline - and today's students will be tomorrow's professionals and scholars. Faculty believe in writing requirements because they know writing is difficult. That's the price we pay for transcending time and space. Writing must be more explicit and precise than speech, because the receiver can't interrupt to ask for clarification. Yet it must also be more concise, in order to justify the extra effort of storing, retrieving, and reading.