Just because the powers-that-be believe diversity is good for them, does not mean they understand that diversity has another side--my post is about what "they" believe, not what "is" true.
But at all events, I am sure the powers-that-be are aware of the down side of diversity, but they also know that so long as people enjoy a minimal amount of prosperity (not too much, though), they will tolerate each other's differences.
Think: most of the racial/religious disaffection comes from the bottom of the economic ladder, while the higher economic classes tolerate and even excuse the worst outrages from the lower classes.
(I'm no expert on Yougoslavia--but might that example actually reinforce what Voltaire said about not having any one segment of the population outnumber all the other segments? Was not the trouble in Yougoslavia in part from a clear minority at odds with a clear majority?)