Looking at a map I don't see why it doesn't have a regular service. Duddeston and Adderley Park seem no more or less deserving.
Because as
Smethwickian says there's little or no demand from the adjacent areas. I remember the view from the station when I first visited St Andrews in the early 70s, with the area up the hill east to the ground covered with terraced houses. On my next visit, it was a deserted wasteland as the area was cleared.to build the A4540 Ring Road, the A45 Small Heath Bypass and the large traffic island. Housing still exists east of these, but is far better served by frequent buses, than trying to cross a high-speed pedestrian-unfriendly road junction to reach the station.
The industrial areas north toward Bordesley and west towards Deritend are most politely described as awaiting regeneration.
The Clements Arms, a basic old-fashioned boozer opposite the station, was always packed to the rafters on match days with crowds blocking the pavement and overflowing onto the road, but apparently in recent years some non-matchdays didn't see a single customer and is now closed.