To win a war with the Horde the Alliance would still have to defeat the vast majority of the Horde still remaining. Which would lead to much more death on both sides, and fighting for years. Varian didn't allow the Horde to pick a new Warchief; he had no choice. While the Alliance would have had an advantage with the Horde being leader-less, someone would have picked up the mantle quick enough, and the bloodshed would have continued...and for what? Most of the most recent reasons for increased fighting, and the "war" between Horde and Alliance is pretty much directly the result of decisions and actions taken by Garrosh; who is now dead (I think/hope he dies). If he hadn't been the Warchief; there would have been no war, period.
So, for Alliance player, enjoy your battle victory that was won in part through working with the real Horde. I'll remember your contributions fondly as I'm relieving myself in the woods of Ashenvale. FOR THE HORDE!