I ran an audio store in 1990s set next to a large USPS center.
Every late afternoon a few UPS and Fedex trucks would pull up and off load their cargo contents on the postal dock. Tom
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.