From our point of view the problem is that existing submissions can be edited after the due date. The real problem with this for us is not that students can alter their submissions but that they can inadvertently make their submissions 'late' when they have in fact submitted on time, by going back in to the assignment. An option to set the assignment to lock all submissions at the due date whilst allowing allowing late submissions for those that haven't yet submitted is what we require. It's the behaviour that I assumed was the case until I tested it.
The 'require students to click submit button' option does prevent this problem but only at the expense of creating a few others. It makes it a two stage process with the inevitable result that some students will upload assignments but not press submit, and also prevents assignments being updated between the upload date and the due date.
Is anyone aware of any current Tracker items that might address this? If not I might open one.