Amusingly, it mostly died off because of a film called An Alan Smithee Film: Burn Hollywood Burn. In that film, a man called Alan Smithee couldn't get his named removed from the film because the only available pseudonym matched his own name, with said film being so terrible that it's own director wanted his named removed from it.
So a film about the use of Alan Smithee as a pseudonym was credited to Alan Smithee, which in turn made it incredibly hard to take the name seriously any more.
When the film was finished, Siegel did not want to take the credit for it and Totten refused to take credit in his place. The DGA panel hearing the dispute agreed that the film did not represent either director's creative vision.
The original proposal was to credit the fictional "Al Smith", but that was deemed too common a name, and in fact was already in use within the film industry. The last name was first changed to "Smithe", then "Smithee"... Critics praised the film and its "new" director, with The New York Times commenting that the film was "sharply directed by Allen Smithee who has an adroit facility for scanning faces and extracting sharp background detail," and Roger Ebert commenting, "Director Allen Smithee, a name I'm not familiar with, allows his story to unfold naturally."
Shame the Eric Idle film couldn't make hay with this.