Cleaner, bigger nicer trains- AFAIK you can't get a train from CP to Streatham Common either, a new bit of track would have to probably be built for that though, through the Streatham Hill train yard.

The circular route that is planned is a joke, as people mentioned, you need to change at Clapham Junction (the LO platform is a joke there too, covered in weeds, even after they closed it for 4 weeks for maintenance). You'll probably be dropped from Crystal Palace/Surrey Quays at Clapham on platform 17, leaving a 1-2 minutes walk to platform 2 for the LO interchange.