I always thought that Eris was supposed to garner sympathy from the Alphies and use it to ingratiate herself as a spy for the Founders, or at least as a more visible
spy, to distract from the shapesifters. Since this failed I'm assuming that particularly unique clone was...retired and a standard clone was used as a behind the scenes facilitator in the Gamma Quadrant.
So the Dominion went for operational phase A2, manipulative diplomacy and they had to find a Vorta as cunning slimy and quick witted as the all too sly denizens of the Big A.
(C'mon, you don't think that the Humans have reformed themselves and become model sentients by the 24th century do you?
Of course later on we meet a Vorta who is rather different in his approach...