Bombing left lots of buildings in a bad state but many were repaired. Just a question of priorities I guess.
The central platform must have been a very narrow island platform. If it existed today, I'm sure it would be closed for safety reasons. If a narrow island platform is full of people and more peple try to get on to it either from an arriving train or via the stairs, there is a real risk of people getting squeezed off the platform onto the track. However, it's possible that it was just removed as part of a rationalisation programme that determined that there was no requirement to stop fast trains at Forest Hill. Does anyone remember?
I recall that Angel station on the tube was completely rebuilt in a new location some years ago largely because both tracks were served from one central platform and increasing use of the station meant that it was unsafe.