Another use for NaN's is, suppose you have an array of sensors. Given enough sensors, you're pretty much guaranteed that some of the sensors will have failed. So the array needs to continue to work, even if degraded.

A failed sensor can indicate this by submitting a NaN reading. Then, and subsequent operations on the array data will indicate which results depended on the failed sensor, as the result will be NaN. Just defaulting to zero on failure will hide the fact that it failed and the end results will not be obviously wrong.