My view on why no stops on or after WADI.. there are a lot of trains to Mumbai from Wadi, GR, Solapur etc.. hence, no specific requirement for this train to stop at these places. Vice-versa -- not too many people from BZA, VSKP etc in these areas also. Hyd connectivity is also very good from these places.
When it comes to Pune -- it is required for people to travel to those parts of Andhra where there is limited train/bus/air connectivity.
Also, if they stop this train at every other station, then...
more... better take a passenger train & not SF :)