I just feel sorry for people trying to board at Brockley. They must feel incredibly hard done-by.
I don't pity them. They should live somewhere more sensible.
It is generally possible to get a seat at Forest Hill (except on a couple of trains), with a bit of tactical positioning to make sure you are one of the first ones on.
Train congestion is a major problem at London Bridge. A small number of incoming tracks serve a large number of terminus platforms - the balance is much better with the through platforms. As for why the busy South London services get routed into the terminus platforms while the Kent and Sussex trains get routed through, this is the way the railway developed, with separate railway companies for the different areas having separate railway stations. Now as then we continue to pay the price for the lack of integration and long-term planning.
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.
Thameslink 2000 is designed (inter alia) to alleviate this.