Tell me, at which platform does the FH 0821/HOP 0824 normally arrive?! When it's on time, that is. Platform 8, you say? The lowest possible? Why, that can't be right?!
As far as I can see, Southeastern trains, or others using the NX-Lewisham branch, proceeding to platforms 8-12 are relatively rare beasts, at least at that time of day, with these platforms generally serving the NX branch. I agree that more trains to CX at peak times is a non-starter for that reason, though.
Anyway, surely extending the footbridge diagonally across to platforms 15-16 would be a good way of relieving congestion at the foot of platform 13 and then worse at the foot of platform 12? Not to mention vastly reducing walk time between (say) 15 and the Tooley Street footbridge exit? How much can that cost? (I know the answer to this is 'a lot more than you think', and I don't for a moment think I'm the first person to think of it, but still).
Trains from here can go to any of platforms 8 to 16 - it matters not which, because there are only a small number of inbound 'up' lines (2? 3? I forget) which fan out into the 15 platforms.
They will use them all so it's just tough if it ends up being 16.
The difficulty is in crossing to platforms 1-6, and vice-versa - hence no Lewisham trains on 8-16 either, as far as I'm aware.
There has been no investment in e.g. an extended footbridge as they have always hoped to get TL2000 off the ground and it would have been viewed as a waste of money.