In the past there sole purpose was to maintain balance between Empires, starting wars, helping empires win/lose wars etc.
I still am fully against the idea of your magical Illuminati guiding the world through political assassinations. Let's say I wasn't against the idea of magical Illuminati, there is no possible way that wars maintain balance. The largest consequence of a war is a massive upheaval of the preexisting status quo; in simpler terms a shift in the balance of power. The only time a war "keeps balance" is when there was a previous war that unbalanced everything, in which case your magical Illuminati are doing a horrible job and should look into becoming just regular assassins.