I lived here for a few years between 2012 and 2015 or so. It was mayhem every morning - a lot of folks arriving on buses (much of East Dulwich rail-heads in anyway, but during that time there were a lot of London Bridge works closures too) - plus hospital users and many interchanging people.
In that time, Camberwell and Peckham also became pretty 'hot' areas of London also - so many more folks visiting for bars, restaurants and so forth.
But while being there, in addition to the Overground, the Victoria-Dartford trains were progressively extended in running hours, extra Thameslink services were added, the Dover service was added - and more peak Victoria semi fasts began to call. So rail use really exploded. The entrance was rebuilt with a crappy temporary building and second footbridge - as forget the pub, but even the surviving ticket office was given over to a (decent) coffee shop). It was a bad a bottleneck and the station manager, a lovely exuberant old gent, definitely struggled with the lack of gates and the crowding.
This is long overdue. It's only going to increase if more services run from Victoria to the Dartford lines, and if Overground is increased to 6tph as mentioned. It's something of a hub now. I'd expect (northerly) platform extensions some day too - for 12 car Thameslink services potentially (a turnback would also be useful, South London needs one for Thameslink).