The USPS has several routes that cost millions per year, using mules ( down the grand canyon ) or airplanes with landing skis ( rural Alaska ). There are thousands of other less dramatic, low volume, very rural routes.
Canceling or substantially modifying these routes carries a heavy political burden, for the recipients are often very poor or native American tribes, or both.
If the USPS is not locked into long term contracts, this seems to be an opportunity for drones. Amazon, unfortunately, has given delivery drones the reputation of being for short-range, very quick deliveries in high density urban areas. But the Ukrainians have shown that drones can be very useful in the 10 to 100 mile range, carrying multi-kilogram warheads. If they can carry TNT or RDX, they could carry mail.
As the high cost contracts expire, drones could be phased in. Mules, airplanes, and gas-powered mail trucks could be phased out. Maintaining drones is cheaper than feeding mules and paying mule handlers, and way cheaper than maintaining airplanes and trucks.
Note that incoming mail weighs a lot more than outgoing mail. ( Incoming mail in rural areas often includes many consumables such as food, fuel, and medicine ) Many of the flights could be one-way, using parachute drops, which are much cheaper, safer, and faster than landing.