The title of "World Champions" is the primary reason that many teams are attracted to the USASF event. As the USASF has decreed that the USASF is the only event anywhere that can call itself a "World Championship" (without serious punishment for the athletes or EPs involved) no one will "replace" Worlds any time soon. Having a monopoly on that title insures that USASF Worlds will remain a sought-after event for many teams. That is not to say that other events could not surpass Worlds in terms of prestige, venue quality, production quality, or value/cost ratio. (Prestige would easily be the most difficult to overcome.)
Many other sports have non-"World Championship" titles that are at least as important to the participants as the "World Championship" event run directly by the sport's governing body. Olympics is the most obvious example for many sports. (Some sports use the Olympics as their "World Championship" for that year, but some have separate events.) Quick examples that come to mind:
Tour de France
The Masters
Wimbledon
Boston Marathon
Indy 500
This strikes as potentially one of those type events for all star cheer. (NCA is already there in many athletes' mind.)
Great Point. Another example is "The Masters". Its the most prestigous and sought after golf event in the world and its not run by the PGA (golf's governing body).