Yes, but it is not that easy. Remember that people who live out in the boonies get the same mail delivery as people in more densely populated areas. Ditto for post offices in rural towns. A real business entity will want to charge people more for delivery in different circumstances. I can just hear the farm state politicians of both parties howling if rural residents had to pay more for their mail service and postage. Once a government program is entrenched, it is awfully difficult to undo.
Ending the postal monopoly is not the same as ending the USPS.
If Fed Ex (or anyone) starts up in a easy-profit market, then the USPS wouldn't have to serve it. This means it could shrink while still devoting resources to areas that private companies refuse to serve.