As a regular user, it does indeed show next train [this/other] platform. It is really only ever an issue in the peak if you end up with two trains overlapping in the platforms at Bank. Even then it is clear and the display shows next train correctly (the other platform will show stand back train approaching)which helpfully allows you to wait for next train rather than cram on the full one waiting to leave.
Regulars tend to hover at the cross passages and wait for route to be set/then look at the displays. I personally am always at the Waterloo end so also listen to the points go over (you can also pretty clearly hear the next train on approach to Bank).