Many of the examples in this post are great examples of 'Modernist Art' and are decidedly not postmodern. This is roughly the equivalent of writing a post on "Functional programming is Anti-Mind" and then demonstrating that with examples from the Gang of Four Design Patterns book.

The real issue with this is that most postmodern art is incredibly accessible. You don't need an art degree to think that Roy Lichtenstein's paintings "look cool", or that Campbell's Soup cans are "neat". One of the quintessential, textbook postmodern film directors is Quentin Tarantino; there are few directors more adored by the general public. Postmodernism is a descriptive term for artists who mostly reject the Western tradition of 'High Art'. Almost all the difficulty and "unintelligibility" lies in postmodern theory, but not in the art theorists consider postmodern. And I would argue that this is because theorists themselves are artifacts of Western high culture and are therefore unable to articulate a response to something that is outside this framework.

Almost all examples of "unintelligible" art fall into some subcategory of High Modernism. High Modernist schools of thought are almost always exploring questions within the context of Western high culture(ie the "What is art?" questions), and for many of these works you need to have a background in the art in question to really engage with and understand the piece.

If you want to critique postmodernism a good place to start is Fredric Jameson's "Postmodernism or, The Cultural Logic of Late Capitalism".