I've found out about IDEF just yesterday and wondered immediately why it's not more popular than UML. Judging from documents, IDEF is at least as suitable for software modeling as UML is, but is mature and stable for about 30 years now, as opposed to UML.
Is this one more case of "popular vs. powerful" like all the discussions about "$language vs. Lisp"?
UML is promoted by IBM who bought Rational Rose the Founders Company
UML is specifically an object-oriented modelling approach, whereas IDEF is more of a an all round modelling approach which supports both business-driven and data-driven approaches. The two can be complimentary. See blog post - http://enablealignment.blogspot.com/2010/01/modelling-its-all-about-communication.html
Why isn't lisp popular? It's more technologically advanced than any language? Really, IDEF isn't popular because it isn't. COBOL was popular because it was. It was good about as much as lisp was bad. Or IDEF.
Popularity is a social circumstance. As a programmer, I thus suppose I have no authority whatsoever to judge what should be popular.