I think everyone is too quick to crown Braig as mastermind. Braig was working for MX before he took Terra's body. In all likelihood Braig is just carying out Master Xehanorts plan. Because clearly as you see in the discussion between him and Terra in the secret ending, Master Xehanort's plan is already in motion and goes further then just taking Terra's body.
I'd most certainly like to know why both Ansem SoD and Xemnas were power-hungry when Xehanort apparently had no memories of his past life of whoever he is. This is a long shot, but I think it might have something to do with what happened between Terra and MX after they both "died"; maybe Terra coveted MX's heart, which held memories, and once the Heartless-Nobody split happened, MX's heart was free to pour its memories into Ansem SoD and Xemnas. Like I said, a long shot.
Though, it's impossible to say that Braig had no role in it all. He's probably the most important member in the Organization as far as plans for power go, aside from Xemnas, of course. And, of course, he wasn't stupid enough to overestimate his capacity against the rest of the Organization, even if he did manage to overthrow Xemnas. He pretty much sat back, enjoyed the view and cracked a few jokes on the way. He had nothing to worry about, that's all.
And you could say that it could've been MX's intention to lose his memories and to have Braig make them all experiment with darkness, but at the end of the day, MX had to make himself very vulnerable to do that. Braig could've looked at Xehanort, laughed his ass off at his amnesia, and said, "You know what, I'm not going to go through with the plan." So essentially, it was Braig -- if none of the other apprentices were involved as you can assume -- who pushed everything forward. Without that willingness, none of this would have happened.
It's just a question of where Braig's cunning ends and where his gullibility begins.