From the end of The Broken Chessboard: Brzezinski Gives Up on Empire:
“…To put it in a terminology that harkens back to the more brutal age of ancient empires, the three grand imperatives of imperial geostrategy are to prevent collusion and maintain security dependence among the vassals, to keep tributaries pliant and protected, and to keep the barbarians from coming together.” (p.40)
It’s rather difficult for the enemies of the Imperium to get together: say, for the Zhodani and the Hivers to draw off Imperial navies, allowing the Solomani to retake Terra and the Solomani Sphere. A lack of an “FTL instant internet” and the vast distances involved, as well as cultural differences, gets major play here.
But it is definitely true that — as a direct result of Emperor Strephon’s insistence on returning full powers to the Archdukes, including taxation and military authority (instead of keeping their powers ceremonial) — the Imperium broke up.
And not in a fairly quiet and low-key manner, like the Soviet and British Empires, but in an absolute bloodbath.