Sometimes, you just want to have reminders or tasks on a contact without necessarily having a specific due date attached to it. For example, I may have to remind myself to check a contract before I speak to the contact next time, so I want to just add the task there, but not attach a due date to it. This enables me to go into the contact and check my "todos" that I can do any time I will work on it next, not necessarily at a specific time that I have to specify in advance.
The workaround I'm using today is that I'm making the due date like 10 years from now, so at least it doesn't look like it's overdue. And I have made a mental note to myself and within our team that tasks that are due many years from now are simply things we have to do whenever we work on a contact next or things to check when we see it, not necessarily at a specific date.