I think looking at our history, specificly WWII (agressor nations like Germany defeated by nations that they brutalized, like USSR and UK) Even if the Fed is weakened, they will make every attempt to 'keep the peace' to the best of their ability. So they won't want the Romulans and Klingons to carve up Cardassian territory as 'prizes of victory'.
One thing that I always wondered is what happened in the Gamma Quadrent: The 'unbeatable' Dominon was defeated, the Founders were revealed and turned out to be not quite gods, and both the Jem'hadar and Vorta have begun to break out of thier roles as slave races. OH, and Odo is there, curing the Changling plague and trying to improve solid/changeling relations. Quite a bad time for them.
Especially if there was any race/group that was a direct threat to them...
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth