AFAIK, the USPS has no legal claims over another carrier’s rights to operate. Interstate commerce is controlled by the US Interstate Commerce Commision, and each state.
And, doing same day in your town is even cooler when it needs to be same day across the country. Last summer on a music video, the label people in L.A. got it into their head to ship- BY AIR- Sugar Glass, used for stunts. They boxed some up, in a wooden crate, and shipped it first thing in the morning NY time- like 6:00 am L.A. time, and it flew against the sun, landing in time for our nighttime shoot.
We opened the box, and the stuff was broken. <grin>. STUPID Producers. At any rate, that was not my first experience with Same Day.
Usually it’s called “Counter-to-Counter” delivery service. If it’s a small box or envelope, it’s run up from baggage to the ticket counter, or baggage counter, and your currier can get it there. Pretty cool. Mighty pricey, but then price isn’t always a consideration. I did indeed have my buddy who lived in L.A. get me a piece of gear in the same day, but it arrived late my time- still I had it for the job the next morning.
I’ve done this by FedEx too, but most airlines have MORE flights leaving for MORE cities per day than FedEx does.