Domestically there has been both UPS and Fedex shipping where USPS does the final delivery. I feel like that’s become fairly common but it only happens at the very end before delivery is made. I had that happen just last week with a shirt from Macy's.
Paid for UPS shipping and the package was immediately sent to the US Post Office.
I shipped something internationally from the UPS Store and I was offered to choose to ship via UPS or the Post Office. UPS was about double the price, but I chose UPS for reliability and good past experience over the years vs. USPS.
The tracking says that the shipment was immediately transferred to the Post Office with a new USPS tracking #.
I paid double. I was never told this could happen. I would have just used the post office.