One more advantage: ZIP codes are a good trade-off if you want to gather anonymous data in a survey or provide anonymized data to an outside entity. For example, we recently conducted a survey on mobility patterns within our university. To offer respondents a reasonable amount of anonymity, we just asked for their (German) ZIP code and the location of their primary workplace.
This allows us to determine the distance and approximate route people would take between home and university campus - to a degree that is sufficient for our goals.