Tomalak said: The only reason the Founder ordered the genocide of the Cardassians towards the end of the war was because she was dying, desperate, and felt betrayed. If they had conquered the Federation in the first few months, none of that would have occurred.
Others see it differently.
In "Broken Link," the female Founder promises extermination of the entire Cardassian people, saying to Garak, "They're dead, you're dead, Cardassia is dead. Your people were doomed the moment they attacked us."
The intent seems clear: The Cardassians as a race will pay with their complete eradication. One might even infer (with less justification, granted) this would have eventually included the Romulans, as well, since they participated in the abortive preemptive strike during "The Die Is Cast." Then, again, perhaps the Dominion had collected intelligence conclusively demonstrating that the plan itself had originated with the Cardassians, and thus wished to exact a particularly demonstrative and definitive vengeance upon them.
Alternately, she was merely posturing---which seems
highly unlikely, considering subsequent events.
Let's fast forward a few years, to "What We Leave Behind," moments after the Cardassian fleet has switched sides.
She announces, "I want the Cardassians exterminated." When Weyoun asks for specifics, she replies with, "All of them. The entire population."
Why would one order genocide in the midst of a battle the outcome of which was still in doubt, when such orders could only result in the masses rising against you (to the limited extent they could)?
Earlier, she had said, "We should've rid ourselves of the Cardassians at the first sign of rebellion." Could that be read, perhaps, "once they were more trouble than they were worth"? I say yes.
Entirely reasonable conclusion: The female Founder accelerated the Dominion's timetable for the liquidation of all Cardassians in an attempt to keep her promise.
The question at hand is this: Did she issue the orders exclusively because of the Cardassian betrayal ... or because she saw the writing on the wall, knew the Dominion could no longer win, and wished to fulfill her vow to eradicate the Cardassians while she was still able to do so?
Could it have been a combination of both?
In my opinion, a quick victory over the Federation Alliance would have resulted in its emasculation, dismemberment ... and then the excision of the Cardassians
the instant they no longer served a purpose. Their world would have been cleansed and employed as a staging ground for further Alpha Quadrant expansion. Who, at that point, would have gainsaid them?