Let's remember that nothing was proven about whether the Detapa Council was replaced by Founders or not. Bashir administered the blood droplet test - but the same test earlier in the episode had failed to reveal that Martok was a Founder! Clearly, the test wasn't worth anything much. Indeed, it was originally suggested by a child (Odo) and supported by a Founder (Bashir) in "The Adversary", and later independently introduced by another Founder (Martok) in "Way of the Warrior"...
At best, Sisko supported one faction over another in an internal Cardassian power struggle, coinciding with an external struggle. At worst, he aided and abetted insidious Founder infiltrators. One wonders if it wouldn't have been better to let Cardassia fall. Certainly it would have been more difficult for the Dominion to stage the later invasion.
Given the known facts at the time of making the decision, though, I'd say the UFP did the right thing in not intervening: Klingons were the more important ally. And not despite because they were unreliably violent, but because
I’m not sure what the point was of the silly “Tailor, take my measurements for a suit” game. When Sisko is intentionally talking about the coming invasion in front of somebody who he knows will convey the information to the Cardassians, does he think he’s not disobeying orders because he’s not addressing Garak directly?
I'd wager that Garak, being Garak, would not have accepted Sisko's evidence unless it was presented to him in this silly manner... He'd have taken it for a ruse. Now that Sisko went to all the trouble to present
it as a ruse, Garak of course immediately bought it. He knew Sisko had to be serious about it if Sisko was being silly about it. That's Garak for you.