It forces you to bite the bullet and really think about how systems must be able to give rise to intelligence, regardless of their physical makeup.
The wikipedia article that you linked has this quote: "The sheer volume of the literature that has grown up around it inspired Pat Hayes to quip that the field of cognitive science ought to be redefined as 'the ongoing research program of showing Searle's Chinese Room Argument to be false.'"
Incorrect arguments are an important step in establishing correct ones, which is a central point of jsomer's argument.