I never realised that working passenger services went through East Putney on the main line. Any reason why they still exist? Parliamentary reasons? It doesn't seem like they go to any Waterloo platforms not easily accessible from the Main Line (8 and 11).
It's a diversionary route for engineering works in the Wimbledon - Clapham Jn area, and has seen all day use every now and again over the last few years. I don't think it's parliamentary in the sense that it isn't up for closure - it may be more to do with maintaining contracted rights for the passenger diversionary capability. Before privatisation it was a BR route with LU running powers, in fact when 'I were a lad' all the stations were in standard SR colours and signage, even though BR never called.
However the main purpose is as an ECS route, and it is apparently essential to the train plan, mainly because it allows trains to get to Wimbledon Park depot in the down direction without having to cross the main fast lines.