Ben , The kind folks on Twitter who I also put this question to agree with you. It appears that this came about with the cessation of guards in the 80's. There was apparently a ruling that all offside platforms (furthest from the driver) were treated as being a Category A platform (requires assisted dispatch in the event of faulty OPO equipment) regardless of other characteristics which, for platform 2 being dead straight would now be classed as Category B platform such as Westbound Central line platform 3 at Stratford with the driver able to see the full length of the platform from the cab.
DistrictSOM , Do they? I only ask because just before the sand drag there are these signs with arrows on them and platform has been consciously omitted for as long as I can remember. All the photos and videos I've managed to find of a Piccadilly train in the centre road shows Platform 3 in use.
Chris M , It should be because version3point1 notes that CCTV coverage of both platforms is provided and OPO mirrors also flank both platform 2 aswell as 3. There are two notices flanking the centre road, the one on platform 2 simply reads "Do not open doors on platform 2" whilst the one on platform 3 notes "The OPO mirror has poor visibility, please make a visual check along the platform edge before closing the doors". I'd assume that the notice on platform 3 is why it is preferred for that platform to be used since it is on the drivers side making for an easier dispatch OPO equipment issues for no longer relevant regulations.