The cost of sending a letter to any address in the US is the same. The cost of delivering that letter varies wildly. Think New York City vs. rural Alaska only reachable by plane. If USPS did not have monopoly, they would be severely undercut in profitable areas and would only service hard-to-reach areas where prices would spiral out of control. So if you want to keep the price of a stamp the same nationwide you need to grant a monopoly. It's the same reason regulated utilities own the power lines.