The Secret World, some of those questions got answered via yesterday's community question-and-answer session on Facebook. While you'll have to Like the page in order to view all of the answers, you're rewarded for doing so with a breadth of facts about the secretive power-mongers and hoarders of secrets.
Among the first questions was the simple one of how the Illuminati aren't in control of everything in the game world if their operatives have infiltrated the highest level of government; as it happens, with the world exploding and lighting up with the supernatural, the Illuminati are too concerned with working overtime to keep things under wraps to try to take total control. The answers also reinforce the idea that the Illuminati crave power and competence above all, up to the organization's willingness to discard lesser members for valuable information. You can take a peek at the full set of answer on Facebook, but keep in mind that you're going to need to Like the page first.