This is already the case in some very small communities, and there are sometimes mail delivery volunteers. The USPS was already profitable but has been undermined significantly: opening the private option for servicing USPS mail and requiring pensions to be paid up front for every employee.
Additionally rural communities are about 20% of the population, and many of these communities are around farmland, which of course is necessary to keep some of. It's much harder to live alone with just a small amount of farmers vs. even the smallest of communities. Should farmers commute to the farm just so the USPS has a slightly easier time?