As for why the trains can't be routed differently, sending trains from East Dulwich / Peckham Rye / South Bermondsey (which come from the southernmost approach tracks) or Forest Hill (the next set across) would mean cutting across other tracks and delaying other services. This is why we only get Charing X services in the evenings and on Sundays, when there is less traffic, and why East Dulwich and the rest get none.
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).