Captrek, you could also use your same logic and apply it to Sisko's POV.
Sisko when listening to Gowron making claims of Changeling infiltration to conquer Cardassia, could not just
be thinking about the consequences of his actions but also all the consequences of his inactions. Think about it. Given what he had just been told by Gowron, can Sisko really
by sure at that point that the Klingon empire itself had not
been infiltrated at the highest levels? Perhaps Gowron himself was a changeling? Is it unreasonable for Sisko to think so, given the fact that Gowron should
know how the UFP would react should he declare war on Cardassia? And what if it turns out it is true (and it did later on, not Gowron but Martok)? Would it really been in the interest of the Federation to have the Cardassian empire conquered by the Klingons who would be under the influence of a changeling? Both
empires would thus be under Dominion influence. And do you not think that an already war-hungry Klingon people, their fires fueled by victory and a belligerent power-hungry Klingon leader like Gowron (who could be a changeling) would not
turn around and declare themselves the most powerful force in the Alpha quadrant and still
break the Khitomer accords?
Given the alternatives, Sisko did not have much choice. The changelings played their moves well and backed the UFP and the Alpha quadrant into choosing the lesser of two evils, and Sisko did do what was right given the information he had then.