UPS and FedEx are two of the Postal Service's largest customers. For some addresses, it's more cost-efficient for them to pay the USPS to deliver a package than to do it themselves. They're content with the arrangement.

All 3 companies prioritize deliveries and choose to deliver packages that were shipped by higher priority, more expensive methods while others sit undelivered. When I bought my phone a few months ago, FedEx put it on the truck but didn't deliver it because it wasn't scheduled until the next day. The phone bounced around on the hot truck for no reason and then was returned to the warehouse, where I picked it up that evening.