While I do not disagree with your first paragraph's description, I would not agree that coherency is a necessary component for profundity. This is something a lot of Modernists realized: much of human experience is chaotic, disorganized, the very antithesis of coherency, and that one could not capture that experience with art that was (at least not too) cleanly coherent. So the Modernist authors invented/experimented with stream of consciousness, poets invented/experimented with montage, polyphonic voices, and other techniques that undermined coherency. Now, the Modernists still often sought to find unifying elements, whether it was religion or tradition, but typically they failed (as Pound said of his Cantos: "I can't make it cohere"). But even before then a proto-Modernist like Whitman had said: "Do I contradict myself? / Very well then I contradict myself. / (I am large, I contain multitudes.)"
The postmodernists, meanwhile, did not seek any coherency but have been, by-and-large, content to treat all artistic history as a playground of toys to be played with to their fancy's content. I think part of that is the result of them growing up in later societies that were already a melting pot of cultures, people, and the arts in which they experienced so much variety without the prejudices and classism of judging some as being "higher" or "lower."