The reason the late night trains run via Cannon Street is due to a possession of the Dn Charing X & Up Cannon St. lines that goes on at 2355 each weekday night. Trains could call at plat 4 London Bridge but would need to be manually dispatched since all the CD & RA equipment has been removed.
They couldn't call there late at night, because as you say there is a possession in the way.
