Please go in and upvote this idea if you like it. I think this would really allow people to use task management as a reminder and customize when the you want to be reminded to do an event as not all tasks can be worked on immediately.
My staff does a really good job of making sure their tasks are clean as that number above their portrait bugs them and they see it constantly. That being said, there are certain tasks that you don't want to lose and want to record immediately, but they cant begin until a certain date. It would be nice if the notification didn't appear over the portrait until the reported on date. This would allow you to put a task on someone for the future and still allow them to keep their portrait icon current. If the reported on date would drive when that notification on the portrait appears, that would allow customization for this feature and work within the existing task management work flows.