I'm talking about such examples as a white, American male comedian making jokes about how white culture is deeply flawed, Americans are deeply flawed, being male is deeply flawed. Comedians like Louis C.K. have become immensely popular and successful while making jokes that hold a mirror up to the face of the dominant race, culture and gender to point out its legitimate flaws (though that's not the sum total of C.K.'s work by any means). This type of self-awareness and self-deprecation by a member of a dominant culture in a society seems relatively historically new to me, especially the major mainstream success of it. Throughout history many rulers have suppressed satire and comedy as being a form of dissent.
Through my (very) basic undergraduate studies in Theatre history, I've read that satire and criticism of the dominant culture through comedic performance has had a long way to go before becoming mainstream. Roman comedy actors were barred from politics and persecuted. Mummers and traveling actors during medieval times were persecuted as well. Shakespeare and his contemporary dramatists kept their satire deeply hidden, or satirized more general subjects. Molière was allowed more flexibility, but still kept under watch by the patronage of the aristocracy.
I hypothesize that the mainstream rise of comedy and comedians from oppressed cultures allowed more space for dominant cultures to do some soul searching and self-criticism, especially given the rise of self-awareness by the dominant. In the United States I'd mark that by the rise of black comedians talking more frankly about race after the Civil Rights Movement. In history before you might have things like Yiddish theatre making fun of dominant cultures, but they were nowhere near mainstream.
In any case, I'd be interested to know about the history of this type of comedy where the dominant culture openly criticizes itself, and where not only is the artist not censored or marginalized but instead becomes mainstream and successful. Furthermore, have there be exceptions throughout history where a dominant culture had condoned or even enjoyed self-critical humor on a mainstream scale?
Roman comedy actors were barred from politics and persecuted.
To some degree, this may be beside the point, inasmuch as the low social status ascribed to them had everything to do with the fact that they were actors, and for a number of complicated reasons this was extremely unsavory to society as a whole.
For what it's worth, occasionally the satire actors (and not just comedians) could provide made them vaguely heroic or seen as worthy voices in the political process, but certainly with the sense that they needed to know their place. Cicero mentions in a letter to Atticus that the first triumvirate have made themselves unpopular by their tyrranical actions, and gives as evidence one Diphilus, a tragic actor, who stood up to Pompey by repeating over and over, apparently to much applause, his line "nostra miseria tu es magnus" -- by our misery you are great, a pun on his assumed nickname Pompeius Magnus -- with what one can only imagine to be an effect firmly pointed at the triumvir. Still, we hear nothing more of Diphilus to the best of my knowledge.
More to my point, though, theatre was not the only satirical outlet available to the Romans. The genre of satire, claimed by Quintilian as a Roman phenomenon (satura quidem tota nostra est), was very much rooted in the privileged sector [inasmuch as the authors were generally well-enough-off educated male citizens, so not the great movers and shakers and capable of expressing jealousy and discontent with their "betters", but certainly comfortable at a level of society at least comparable to the stereotype of the modern stand-up] expressing their concern or frustration with the foibles of Roman society. Juvenal and Horace in particular are well known as greats in Roman satire -- if you haven't, consider a read of Horace's satires with the understanding that poetry doesn't always translate so well -- and Horace is certainly happy to namedrop his close connection to Maecenas, the wealthy unofficial minister of culture to Augustus.
Augustus in particular is an interesting study, certainly sponsoring court-friendly art and not leaving the reins free (Ovid's carmen et error come to mind) in terms of literature, but allowing and even indirectly sponsoring certain works (Livy's history, portions of the certainly overall-Caesar-friendly Aeneid by Vergil) that were quite critical of his rise to power and rule.