^Well yeah, but given Sisko was pretty much running the war effort, you'd think they'd tell him these things. 
I think the speed of events is key here. Without the three year cold war first, Starfleet may not have been so prepared. What if they didn't know who the Founders were ? The Founders blew a significant advantage by revealing themselves. With that advantage, they could have launched a co-ordinated attack on key installations throughout the Federation and the Klingon Empire.
We know from what really happened that Starfleet was having trouble with ship production and manpower, that disadvantage could have been worsened if suddenly multiple shipyards are sabotaged or even destroyed by Changeling infiltrators.
Of course, ultimately they always said getting Odo back was worth losing the entire Alpha Quadrant.

I think the speed of events is key here. Without the three year cold war first, Starfleet may not have been so prepared. What if they didn't know who the Founders were ? The Founders blew a significant advantage by revealing themselves. With that advantage, they could have launched a co-ordinated attack on key installations throughout the Federation and the Klingon Empire.
We know from what really happened that Starfleet was having trouble with ship production and manpower, that disadvantage could have been worsened if suddenly multiple shipyards are sabotaged or even destroyed by Changeling infiltrators.
Of course, ultimately they always said getting Odo back was worth losing the entire Alpha Quadrant.