The USPS is a coercive monopoly. Coercive monopolies are consistently poor performers in all the areas that we would care about, like efficiency, customer service, innovation, quality, etc. The reasons for these dynamics should be obvious to most people (I'm a social psychologist, so organizational psychology is super fun for me, but you don't need to be any kind of researcher to understand why coercive monopolies would tend to perform so poorly).
The reality of coercive monopolies' poor performance is something people should be able to process and move forward with without much resistance. It shouldn't take us 200 years or what have you to learn such basic background facts about human organizational factors. But we see a strange Stockholm Syndrome with the USPS for ideological reasons, and that's frustrating. There's no excuse for the postal service's awful performance, and we shouldn't be making excuses for coercive monopolies in general – we shouldn't be wasting time, as a society, with organizational setups that we know are inherently bad.
The USPS monopoly is specifically on "letter mail". That's why FedEx, UPS, DHL, etc are allowed to deliver packages. The USPS uses the mail monopoly to its advantage in pricing package service lower than the private carriers (the monopoly mail routes are fixed, so adding package delivery to those routes is much cheaper than building such routes only for packages). There's also an exception for "urgent" matter, which is why those companies are allowed to offer express letter mail type services.
It's actually illegal to use private carriers to send letter-mail-like matter (documents) if it's not urgent. That's obviously way too vague and subjective to base a law on, but the USPS has actually tried to enforce it at various points. About 10-20 years ago, USPS inspectors were searching the contents of corporations' outgoing private carrier express envelopes (FedEx mostly) to determine if they were in fact urgent. Yes, they were in corporate mailrooms trying to decide whether some material was urgent or not. (I think it was in NYC – it was in the news.) I'm not even sure if it's theoretically possible for third parties to determine whether communications between two other parties are "urgent" as some sort of objective fact, but that topic takes us well beyond the level at which the USPS would normally be expected to keep up with.
There's nothing about mail, shipping, logistics, etc that requires or suggests a coercive monopoly. Having a government monopoly on mail delivery is as arbitrary as a government monopoly on dry cleaning, package delivery, or canned soup. Mail delivery isn't what economists call a "natural monopoly", like a city's running water or sewage system, where realistically only one such system could or would be built in a given area, and multiple competing sewage systems wouldn't be feasible.
Size only makes the USPS worse. It makes any coercive monopoly worse. It often makes private companies worse too, though in some cases the economies of scale make certain achievements or technologies possible (e.g. Apple and the iPhone – they achieve stunning performance by designing their own chips from scratch, which wouldn't be possible without their size and profit level.)
By the way, there's an awesome story about an awesome dude who tried to compete with the USPS. Lysander Spooner founded the American Letter Mail Company in 1844 out of frustration with the US Post Office Department (they changed their name to USPS in 1971). He offered much lower rates (US Post Office Department was charging 25¢ for Boston to DC letters, a fortune at the time) and probably better service.
They got Congress to shut him down in 1851, formalizing their monopoly privilege.
Fun task: Try calling 1-800-ASK-USPS, their main service line. See what happens when you do. Try asking someone anything. I was stunned at what I discovered calling that number – it was unlike any 800 number I'd ever dealt with.