This hints at the real reason the postal service is so important to hold on to. They have a mandate to deliver to every person in the country no matter what.[0] They run huge losses to do this, but it's an invaluable service subsidized by taxpayer dollars the same as any other infrastructure. A private company has no incentive to do this if it's not profitable. People in rural areas and unconventional living situations will get screwed.
[0] https://about.usps.com/publications/pub100/pub100_020.htm