The two big reasons I've heard agents market properties this way is 1) a marketing tactic to generate more calls and 2) at a seller's request for privacy or fear of theft. There is now data to support that you will actually get more contacts if you do show the address. Hopefully this data will fuel the seller's desire to get the home sold and overcome their security fears.
It was found that properties which DO display receive 6 TIMES the page views that properties that hid the address. Further, properties with the address displayed also recieved 6 TIMES the inquires.
Why is this? 3 main reasons:
1) Map search - Today almost every real estate site has some kind of map search, as well as a list search. On Zillow, if we are told not to display the address (NDA), it will appear as such in the search results - but we can't display it at all on a map (essentially giving up the location). Map search is a VERY common and comfortable way for people to search. The map drives many page views into a particular property, and NDA properties miss out on this exposure.
2) Mobile search - Many mobile applications have GPS enabled search to answer the question "what is for sale around where I am right now". Without being able to map properties, again it would reveal the location, NDA properties are missing out on the huge opportunity of mobile exposure. This one will continue to grow in importance.
3) Search Engines - We all know that search engines are important website visitors that can't be ingored. There is huge opportunities for specific addresses to be found in search results, and this likelihood of this grows as people become more specific in their searches - even searching for actual addresses. Again, if the address isn't displayed, Google can't see it, and can't serve it.
All three of these significantly contribute to the amount of traffic a listing will receive if the address is displayed verses if it is not. The exposure loss can be huge. And with less page views, obviously comes less inquires.
In pulling the numbers, one thing that did surprise me was that the percentage of times someone did send an inquiry was actually the same if an address was displayed verses if it was not. So this contradicts the idea that hiding the address generates more responses. My guess is that the people who do reach out to find out where the property is located must counteract those who are annoyed by the lack of data or discount the property altogether because the location is hidden.
* I pulled these numbers from Zillow, as it is a database towhich I easily have access. But I would believe that the numbers are relatively comparable to other websites on which your listings are appearing.