Writing manifests a plethora of intentions. A great programmer of Dykstra's type is also a pedagogue.

For this discussion, considering the association of code with prose in the practice of the software developer, I would suggest that it's really about controlling the generation of entropy. Great prose (Plato's Republic or Locke's Two Treatises on Government) can organize the behavior of an entire culture. So it is with software - particularly when it encapsulates expertise that empowers users to perform well beyond what they could accomplish without the tool in hand.

So one reason that the great programmer must also be a master of prose is that software influences the behavior of other developers and users. Unless they have access to prose that prepares them for effective interaction, the work of the originator is bound to be undermined or ignored.

Pairing a great programmer with a good technical write may be another strategy, but that works in the long run only if they are tied together at the hip.