Well, the only Alpha Quadrant power that isn't in the war yet that has appeared a lot are the Ferengi. And I don't think them joining would be all that impressive. So it had to be a species close to aliens of the week in any case.
This is one of the times, I think, when DS9's unplanned nature hurt it. If the writers had planned the Breen joining from the beginning, they would've done the occasional episode with them