There are many reasons why you might not want to assign writing in your courses. And many of those reasons have to do with limits on your time. Designing writing assignments and responding to student writing take valuable time lots of time if you do them carefully. The larger the enrollment is in your classes, the more time responding to student papers takes. You have lots of important course content to cover, so you have limited time for building in a sequence of writing assignments and some instruction around those assignments.