but...why? Is it because interfacing between digital and analog representations of data, because of legacy systems, why are printers so annoying compared to screens and networks?

Does any place still use HP laserjet II-series printers that gave that error? Those things were workhorses but it's been 25-30 years.

Besides, this error isn't that bad: it means "I've been asked to print something on letter-size paper, but I don't have letter-sized paper. Please load some." Either give it some paper of the size it wants, or check that the paper tray it has is properly set to "this is letter-size paper" and not to "this is A4-size paper".

That's the real cause of why this error was so common: US letter paper and A4 paper are almost—but not exactly—the same size, and there was a switch on the paper tray you had to set to tell it what it was loaded with, and the printer refused to print on the wrong-sized paper. In other words, PC LOAD LETTER is just another entry in the list of things that are frustrating and annoying because the US never adopted metric.

You want something annoying try PAPER JAM IN AREA 3, where you have to open the thing up carefully and hope that the paper doesn't rip as you remove it also be very careful not to touch that one spot that is super hot and will burn you. This was usually caused by someone somewhere deciding to save some money and order everyone the cheap, crappy paper that did this all the time instead of the good stuff.

I haven't had an error like that from a printer in at least a decade. In my office it's been a simple, send to the print queue, scan your ID on the printer and it's there waiting for so long now.