I had no idea this was happening. FedEx and UPS apparently pay the postage on stuff they've been hired to deliver in rural areas so they can mail it. Because _they_ don't want to drive around on crap back roads either, and it's cheaper to pay postage than deliver it, particularly given the damage their vehicles would take.
Pressure on USPS to break even or make a profit is essentially a decision to reduce services, a decision that would disproportionately affect people who live in rural areas, but would affect everyone.
Notice this is happening in a world with substantially less than $4/gallon gas. I cannot believe that more expensive fuel costs would make this less common.
ETA: In the comments, someone noted that the last Harry Potter came out at midnight on a Friday. They had ordered from Barnes & Noble which they say only uses UPS. Except in this case, they used USPS so the book would arrive on Saturday. There are other examples as well.