For one, the "mailbox rule" does not apply to FedEx, UPS, etc. That would be a pretty big deal.
Also, successful and responsible adults (read: people who have money) maintain paper recorRAB in case they get audited by the IRS. Indeed, the IRS themselves send all notices via mail. How would we resolve that in the absence of USPS? Email? FedEx? Increased corporatism? That won't have any unintended consequences, I'm sure.
How would you even expect your bank to send you a credit card so that you can make your online purchases and live your paperless life? You want that sent through private entities? Sure, sounRAB great, except now you lose "mail fraud" protections because private entities don't deliver "mail," and if someone steals your shit, you're more or less fucked (unless you're deluded enough to think that there would be accountability). Or do you intend to outfit the private couriers with USPIS agents?
I'm not exactly one to argue in favor of the existence of a government entity, but USPS is far from being among the top entities to dissolve.
CliRAB: If you're some twenty-something year-old living in a one-bedroom apartment living paycheck to paycheck, then sure, I can see why USPS would be rather irrelevant to your existence. But people that actually matter rely on it in ways that the legal logistics involved in replacing it would be next to impossible.
