When copying an assignment, a quiz or a whole course, any overrides for groups follows with the copy. Those might even be date/time specific, most likely making them not only obsolete but also causing trouble..
This is a trap easy to miss out on when looking through the settings and we've had more than one case of this, causing exams to fail.
The (almost) same goes for start-, end- and stop times and dates, and this also includes Workshop.
It's not very likely that the user want the same dates/times for the activities in a copied course, or for activities copied within a course. Instead it might cause trouble, even if those settings are more obvious in the activity settings than the overrides are.
So, the date/time settings seems to me as if they were best left deactivated when copying a course or an activity within a course.