Semi concede the point KingDaniel, while my knowledge of EU-Trek is above nil, it likely isn't as extensive as yours. If you include the source books for the various role playing games going back to the 1980's, the Federation becomes far larger and more powerful entity than what little we saw on screen. Beyond even the Dominion War Starfleet.
Plus, the Federation will alway have two important advantages over the Empire. One, Starfleet would find a valuable ally in the rebel alliance. Two, it would never be necessary to actually defeat the Imperial Starfleet. If you kill the Federation president and the upper members of the council, the Federation would simply replace them, disruption would be minimal.
If Starfleet (or S31) kills the Emperor and his top "henchmen," any war would end with their deaths.
The federation would leave the rebel alliance to pick up the pieces and go about their merry way.