If losing a mere $2.2 billion last quarter is any indication.
Daily delivery and pickup at every address in the US is bound to be unprofitable; that’s part of the reason the government was authorized to establish it (in Article I).
However, if I were in charge, I’d stop that nonsense immediately, and move to emulate what Japan Post does.
If you’re receiving mail, it’s delivered to your house (just like we do now); otherwise, the mailman doesn’t show up. If you want to mail something, you either take it to the post office yourself, or drop it in a mailbox (in Japan, each neighborhood had a mailbox that you could send mail from, if you already had it stamped, IIRC).
Given the amount of junk mail that goes out, this might not work; it’s bound to be more cost effective than what we’re doing now, though.