<< When you have no competition, your company suffers. >>
This is normally never the case. Theoretically, in any situation where one company is the only supplier of a product with any demand, that company will flourish because it can set the market price wherever it wants, namely where profit is at its maximum.
In this case, there is actually some competition for parts of the USPS' business (in the forms of express carriers) and there must be other forces (gov't price ceiling?) outside of normal supply/demand that are holding the price of regular mail down.
Seriously, what would companies do if the USPS said, OK, we need more revenue, 95 cents for all first class mail now? They would still have to use the USPS, because they are the only company with the existing infrastructure to deliver all the mail, and people need mail delivered in a real bad way. 95 cents would still be 10 times cheaper than FedEx to get your letter there in a few days.