Forgot which Civ was it(was either 3 or 4) where I tried something similar like this but all of the other Civs suddenly decided that I was a giant jerk for wiping out that last opponent and didn't want to vote for me anymore. Oh well, just had to "convince" them the hard way. :p
Civ V is the only one I've ever played. I'm pretty sure in that one, diplomatic victory is more of an economic victory, as there's no possible way to get another country to vote for you, only city-states.
If I can't get a diplomatic victory and have to crush one nation then I may as well just crush all of them because crushing nations in Civilization is like Pringles - once you pop, you can't stop.