I'm quite happy as a craftsman myself. The problem is the many and diverse meanings of the word "art". At the start of Knuth's speech he quotes some ACM worthy as saying that programming needs to transition from an art to a disciplined science. Here, "art" is used to mean something that involves guesswork and holding one's finger in the air. In the title of TAOCP, on the other hand, Knuth seems to be using the word to mean "craft", as in the Art of Fly Fishing. Neither meaning refers to the practice of fine art. AFAIK no one compares engineering to musical composition or poetry, and engineers don't seem to lose much sleep over it.

The functions of art include philosophical enquiry and invoking a sense of immanence in the receiver, and so on; creating a program might cause some of these things to happen in the programmer, but only as a coincidence. In his poem called The Scent of the Real, Alvin Pang writes "to bear clear witness/to your longing alone/[is] the only art/there is." Software doesn't do it either, other than as a potential medium for visual art or other forms. It seems likely that new, distinctively digital art forms will evolve, but even then it won't be "the programming" that corresponds to "the art".