Being able to create announcements anytime and schedule them for delivery is very helpful. The same functionality for messaging, in general, would also be helpful.
Specifically, I message students two days before a quiz is due if they have not made at least one attempt at the quiz. It would be helpful to set up this message and schedule it and move on with the course. Set it and forget it. My students appreciate the message but setting reminders to in another app to remind me to send a message in another is painful.
This is the specific place where I would find this addition most useful