The USPS hired FedEx several years ago to handle a sizable chunk of its express deliveries. The relationship is working very well for both companies.
I use priority mail regularly plus the tracking feature and the price is far less than UPS......
No complaints about our rural post office.
Actually, FedEx supplies the linehaul (airport to airport) for most of the Express and Priority Mail. The USPS still does the pickup and delivery with the customer. But you're right - it has been a "win-win" for both organizations.