You got it backwards -- FedEx has contracts to haul low-priority USPS mail, not the other way around, for about 10 years now. In fact this has brought USPS reliability and timely deliveries way up. FedEx would be insane to depend on the Post Office for delivery of FedEx packages.
DHL uses USPS which is horrifically slow. I finally just started putting on the order “Delay as long as possible”.
It comes immediately.
No I don't have it backwards. It may be the case that they have such contracts. However FedEx also has a low-rate ground service where they pickup a company's packages and those packages are subsequently delivered to the USPS for long haul ground transport and eventual DELIVERY. This was explained to me BY FEDEX when the first of many lost or overdue packages I've had in the last year was three weeks overdue. I have already instructed suppliers that I do business with to NEVER use that service/rate.