Currently if there's a problem that causes a backlog in the message queue, predue/due/overdue notices may not go out in a timely manner. With bug 31453 the ability to limit in the cli was added, but it seems like the default should be not to send these after a certain amount of time, unless forced. This keeps patrons from getting multiple emails at the same time if a backlog occurs and say the predue and due notices both get sent for an item on the same day. I think ideally there would be a syspref so staff could change it if they wanted to as well as a report for anything that would have otherwise sent so staff are aware.
+1 for more checks on what gets sent out via process_message_queue. Untimely messages is a thing that can make patron and librarians pretty upset.