Yes it is.
It is their mission, as spelled out by Congress and the Constitution.
Flat postal rates are definitely not spelled out in the Constitution. And claiming that it's fair because the statutes that govern it say so is very dangerous logic. That's like saying that welfare, or the NEA, or Roe v. Wade is fair because the law says it is. "Fair" and "legal" aren't the same thing. If they were, it would be "unfair" to change any law, ever.
"Fair" in this context is "most efficient allocation of resources." Resources are most efficiently allocated by private enterprise, except in the case of a natural monopoly, which, as several astute FReepers have pointed out to me, postal delivery is NOT, because the USPS does not require tax subsidies to do its job. Therefore, privatize = fair.