The Cardassians made sense for a lot of reasons. They were a major power, yet the withdrawl from Bajor and their failure to deal with the Maquis were symptomatic of their declining position in the Alpha Quadrant; meanwhile, the destruction of the Obsidian Order and the transition to a civilian government left a huge power vacuum, which helped Dukat seize power. The Klingon invasion was, of course, what finally pushed them (and him) over the edge. As he said in "Return to Grace":
There was a time when the mere mention of my race inspired fear. But now we've become a beaten people afraid to fight back because we don't want to lose what little we have left...
On a practical level, Cardassia's proximity to the wormhole and Cardassians' sense of order also meshed well with the Dominion. I just can't see any other major race taking their place without some major fleshing out and explanation.
As for the Breen... frankly, any Mysterious Alien Race could have taken their place. We'd seen them in the internment camp and there had been a smattering of references to them (including in the episode I quoted, IIRC), but there was nothing in established canon that made them particularly well-suited for the Dominion or described them as the fierce fighters with mysterious biotechnology and an energy weapon. That was something the DS9 writers made up.