Have you ever struggled with letting someone else do something that you can do faster, better, and with less effort? If you really think it through, you know that if you don’t pass the task on, you'll be doing it yourself forever.
If this task is in fact the best use of your time, then maybe the staff member isn’t needed. But if there's a better use of your time, then you have delegate it to someone else who will do it slower, not quite as good, and with more effort. You have to let go of the vine*.
How much of your week is spent doing these types of tasks?