I never understood the need to get, and pay for, door to door mail service 6 days a week. I'd happily keep door to door mail service (mailing a letter from my home to someone across the country for roughly 50 cents is pretty great).
As less and less comes through the mail, why not keep up the nice service, but make it like the garbage? They work 5-6 days a week, the post office could be open 6 days a week, but they only come to any given house once or twice a week. that way, you could have far less fuel, mail carriers, etc, you could still drop mail in a streetside mailbox or a post office if you wanted it to get picked up faster, but you'd only have your incoming mail dropped off 1-2 x per week.
this seems like a HUGE savings, that wouldn't really slow mail down that much, as the sorting and long distance trucking could keep going 6 days a week. You'd take out most of the cost, while taking out perhaps 10% of the utility.
you could also choose to have higher service for businesses (either every address in a certain district gets more frequent service) or that any address can choose to pay extra ($20/month?) for "daily" pickup/dropoff service and everyone else can choose to go to the 1-2x per week.