Agree to an extent, and disagree to another. Let me preface what I'm about to say with "If there is Illuminati"
The part I would contend is this idea that The Illuminati would want to stay shrouded in secrecy. Sure actual members would not want to be revealed, but continuing to promote this idea that they are an all powerful, all knowing organization running the world magnifies their capabilities to an even larger extent. As a benefit, it makes some people paranoid, and paranoid people are easier to use because nobody takes them seriously. Who knows, they may not even be that powerful in reality, but common perception is far more powerful than reality.
This is basically the 9/11 conspiracy episode of South Park ending. The idea is tried and true... and parallels everything from Wizard of Oz to Game of Thrones in that by simply seeming all-powerful you gain power you wouldn't otherwise have. So on the surface, I agree with you completely... if you didn't have power the best way to get power would be to seem like you do have power so people defer to you.
The flaw is that no matter what way you try to slice stuff in the modern day world, it doesn't work out that way. To my original,
if you actually had a "World Order" of some sort that was all powerful and could control literally everything, you'd want to keep that a secret or you'd eventually have a revolution on your hands. To your scenario,
if an "Illuminati" existed that had sparse power but wanted to seem more powerful than they were, they simply wouldn't be going after young & low IQ Youtubers and Twitterites in a subliminal pop culture campaign. That would do them zero good. They also wouldn't steal banal buzzwords from a Dan Brown novel/movie for branding. These people are irrelevant sheep and irrelevant to the end game of "control" or "power". What they
would do in your scenario is direct "mysterious" power plays with people who control natural resources, liquid capital, political power, etc. where they represent having more strength than they do in order to get a desired outcome.