Don't forget that if Starfleet hadn't gone through a build-up in response to the Borg threat, then the Dominion might not have considered the Federation a threat in the first place and the Dominion War might never have happened then. It may sound a little implausible, sure, but no more so than the Founders suddenly calling the war off and accepting defeat simply because Odo linked with one of them...
"We think we've come so far... Torture of heretics, burning of witches - it's all ancient history. Then, before you can blink an eye, suddenly it threatens to start all over again..."
- Captain Picard, "The Drumhead" (TNG).