^ Which is another reason I compared them to the July 20 plotters who mistakenly thought that if they took Berlin they'd control the rest of the Reich.
As for Leyton's grand plan? Sisko by himself thwarted it which means that he wasn't on solid ground to begin with. If he takes Earth, so what? You'd have the majority of Starfleet being told to accept a military junta. While your typical Federation officer seems docile and submissive to authority, I don't think they'd just shrug when they find out the president has been overthrown. To say nothing of the governments of the member worlds.