Other than looking "salty" I can't imagine why anybody would want a carrier like that on an F-150. As others have said, there's plenty of room for a decent size spare in the stock location.
You can get a 36 gallon fuel tank on an F-150 from the factory so there's not even any good justification for trying to use the factory tire location for extra fuel, like there is on some vehicles with smaller tanks.
Biggest factor is the way such a carrier interferes with trailering, loading stuff in the bed, etc. On a smaller vehicle (Tacoma, 4runner) without a lot of space, people are willing to accept the hassles of the exterior tire carrier despite the challenges. On a full size vehicle they see no need for it.
You observed that the F-150 is the most popular truck in North America (actually I think it's the most popular vehicle, period.) And yet, even as popular as it is, nobody makes a swing out tire carrier bumper - so, doesn't that answer your question right there? The reason nobody makes one is because there's no demand for one.
BTW I'm not aware of a swing-out tire carrier bumper that is available for a Silverado, Ram 1500, Tundra or Titan either, for the same reasons: (a) It's not needed and (b) it prevents you from using the truck as a truck.