Personally as a user of SE, I'm sceptical on what any takeover will now bring (TFL or otherwise). Having seen the service run by BR, Connex, South Eastern OLR, SouthEastern, I believe due to bottlenecks elsewhere on the tracks (lewisham/london bridge/etc), length of platforms / bridges / etc, there are limits on what can be achieved.
Oyster is already accepted, the stations are in Zones, and sometimes the PAYG fares are lower than rail only fare. So if TFL did take over, other than a new Orangle colour scheme, I'd expect benefits to be limited especially considering TFL's current financial predicament.