Thats a helluva business plan. Our sales drop, we must maintain the work force, so we jack our end product prices up.
Ya, that's gonna work.
The ohter side of that is that they exist to offer a service, but aren't allowed to charge what it costs to actually deliver it because Congress, rather than the organization providing the service, controls the pricing. Anything remotely like a business plan would have to start with free market pricing.
Replacing the USPS with UPS or FedEx strikes me as a ridiculous idea, workable only in the densely-populated areas where the allegedly-Conservative talking heads on TV who support it live in blissful ignorance of anything west of Philadelphia. Those companies deliver a great service but it's not cheap and it basically cherrypicks a part of the USPS customer base so that they aren't really doing the same thing at all for the most part, i.e. what makes up all of their business makes up only a minority of the business USPS has to do. They are basically couriers (High volume, highly-automated ones, but still just couriers), not mail services.
Privatizing the postal service on the other hand could work, but not unless the enterprise taking it over had price freedom on the postage. I don't believe that would make it actually go down, just the opposite, though if it just stayed the same the overhead in USPS would have to be cut drastically by the new operator.