A few minutes of Googling didn't turn out what I was looking for though. I can see an "upload and print" feature on FedEx website, I can see a dedicated mobile app that apparently can print files via FedEx...
... but what I was looking for is something that pretends to be a normal printer, so when i do File->Print in Word or Photoshop, I can choose it as a destination, much like we used to do with "PDF printers", which were programs that installed as printers but outputed PDF files, back in times when MS Office couldn't do PDF export.
So if I'm missing an obvious hyperlink to that, could you please help me out here and post it? ;).
In general, I don't want print shops to start making mobile apps or (even worse) desktop apps to "streamline the process" (i.e. scare the shit out of the living with crappy UI and "upselling opportunities"). My dream is for them to integrate into the system, like every self-respecting piece of consumer hardware does. In the end, I might even not care at all which print shop is doing the job (much like I don't care where I order Asian cousine - those restaurants are all commoditized - I only care about it to be hot, tasty and delivered on time). In a perfect world, I'd love to have it reduced to a single argument, a drop-down in printer settings dialog (but I'd happily accept a system printer per printing shop for now).
I'm pretty sure that FedEx Office (formerly FedEx/Kinkos) has supported doing that for many years. I suspect they aren't alone.