A setting I would find very helpful would be to allow or prevent late submissions based on the due date.
I have stopped using the available/unavailable date in assignments for a few reasons. Mainly, the dates for this setting do not update if you move the assignment in the calendar. They also do not update when importing a new course and use the adjust dates tool.
I think it'd be much easier to have a checkbox in on the assignment settings page for this control. It could be as simple as "Prevent late submissions after the due date."
