In reality, when you send a letter, you are placing it into the care of the postal service. Your letter is only handled by postal employees, and mailbox privacy is codified in federal law. There's clearly an expectation that the postal service is not releasing your information to third parties without your consent. The information on the outside of the envelope is not meant for, nor is it needed by, anyone other than the postal service
Nowhere does it say that post office employees are the only ones who can handle your mail, and in reality the postal service has a ton of contractors that also handle the mail. They do stuff like bulk delivery and OCRing hand written addresses.
A friend of mine contracted with one of the companies that does the hand writing recognition, and if the computers can't recognize an address then a picture of the envelopes get sent off to a team of data entry people who see the address on a screen and type it in by hand.
It's also fairly common for delivery people to screw up and deliver mail to the wrong address, especially in large apartment complexes.
There's also nothing special about postal employees. Why would you trust them more than anybody else? They're bound by the same federal mail tampering laws as everybody else, but nothing above and beyond that.
"When did you last receive a piece of mail from your Cancer / HIV Doctor?" -> leverage knowledge to extort patient
"When do payroll checks arrive?" -> break into building on that afternoon and steal checks
But the situation isn't hard to understand. The entire building has a single code, and the delivery guy is responsible for inserting mail into the individual lock boxes, and he reads the addresses off the envelopes to decide where it goes so he doesn't need a code.
I do agree with your sentiment, though. They know it won't work as expected, so why did they allow you to sign up?