I lived in Wimbledon for 10 years, and 2 or 3 miles from there for another 9. I think I know what I'm talking about. I'm no more of an "outsider" than you are.
You on the other hand are talking about switching from a train that gets in to Clapham Junction from Wimbledon on platform 13 and...
Why would you bother with making a change from Wimbledon when the District Line takes you straight to Fulham Broadway? You'd save about 5 minutes faffing about with trains, whereas the tube from Wimbledon you'd just get a coffee and sit on a guaranteed seat as it's the beginning of the line.