Having your tasks in an organized system saves time ... sometimes a lot of time:
Far less time is wasted on organizing and prioritizing your personal to do list. All your assignments are in a single place. And you can pop tasks into your personal "hot list" so you can focus today’s energy on a specific, manageable set of high priority tasks.
Far less time is wasted on scoping out a new task and tracking down the details. The details are already consolidated in one place for you.
Far less time is wasted on tracking down tasks that are currently assigned to other team members. Getting work done through other people becomes far simpler.
Far less time is wasted on rework. Better communication with all the players involved makes it far easier to get the job done right the first time.