Big question. Multifaceted. Communicated intention is still very important to most artists. I think most wish to still communicate. Why call something art if it not visual? Isn't purely conceptual art just philosophy? Isn't auditory communication music? Isn't written communication writing? How can you separate the visual art from the visual? Conceptual art without the visual, auditory, tactile, or written is simply philosophy. Am I interpreting your question differently than you intended?
I like the definition of communication provided by cognitive scientists that it is a two-way flow of information and that information is that thing that resolves our uncertainty. I think if you think in these terms then the role of contemporary art, as with all art (as Neil suggests, the medium is not the issue) is to act as a communication medium. Did you have any more specific thoughts in mind when you asked this question Elaheh?