If the front of the train knows where it is going, it is because somebody or something has directly or indirectly “told” the front of the train where it is going. So it shouldn’t be beyond the wit of TFL or the company operating the train to also find a way for the same “somebody or something” to directly or indirectly tell the station indicators where that train is going.
However, the sign makes the totally false presumption that the information on the front of the train is correct, but that isn’t always the case. A train from Liverpool street went all the way to Chingford despite saying on the front it was for Enfield Town, and announcing at every stop, both verbally and visually, that the train was for Enfield Town. From Hackney Downs where the lines split, it even announced “this is Seven Sisters/Bruce Grove/White Hart Lane etc”, each time picking the name of the next station from the Enfield branch instead of the Chingford branch.
On numerous other occasions I’ve been on a train where the announcements go “backwards” along the line, ie they’re for the up line instead of the down line.
I wonder, do the drivers know where their trains are going, and are they capable of reading the signs on the platform and working out that they’re different from the names that their announcements are making?