Mail needs to be delivered daily (preferably seven days a week). Economic transaction efficiency depends on the mail. Many invoices, payments, legal documents etc are still sent through the mail (even though they should be electronic).
Saturday and Sunday thus are not required.
As for legal documents, those are all based on the standard work week as well, so that argument falls as well.
As such there is no reason for mail to be delivered on Saturday or Sunday. At the company I work at we get mail on Saturday, we don't get to read it until Monday anyway.
No, it doesn't. Quite a few legal documents are signed on Saturdays and then overnighted back so that the sender can have it back by Monday.