I agree with both the points made around lines of communication. I'm just kind of thinking of using the postal service as a way to get out information as to what services are offered or how people can go about getting special delivery privileges.
I also agree with Kimberley's point on the difficulty around a one-day-a-week delivery mode in terms of getting notices for appointments and things like that. A letter comes out the week before to tell you about an appointment that you have the following week, and that's a very difficult turnaround when we're talking about only getting your mail once a week. That's definitely an important thing to keep in mind.