I think this is somewhat similar to the situation at, for example, Portsmouth Harbour, where the train to London Waterloo via Eastleigh isn't shown as destined for Waterloo, but shows Farnborough instead. In that case, apparently, experience has shown that enough people who want to go to London have in the past made the mistake of thinking that a train that used to be shown for Waterloo was the one they wanted, even if it also said "via Eastleigh", and got on that instead of the Portsmouth Direct Line. It would be sensible to to do something about the situation at Clapham Junction, so that there'd be no risk of someone what wants Southampton thinking that the "next fastest train" will get them there soonest, when in fact they'll arrive more quickly by changing at Woking or Basingstoke.
At Clapham Junction it may well be, as several posters have said, that a traveller bound for Southampton has looked up the details in advance. But what if they are delayed on their way to CJ, they arrive and check the screens to find out what platform their train goes from, and they see this "next fastest train" displayed? They quite possibly don't know that there's another route via Chichester etc. It will seem that the info they looked up beforehand perhaps wasn't entirely right. They don't want to miss the "fastest train", so they'd better get this one rather than make enquiries. At the very least, to someone unfamiliar with the routes and timetables, this display is potentially confusing.
The sensible and most helpful thing would be not to show the 16.42 Southern service, but to show instead the next fast train to Woking or Basingstoke, as appropriate, with advice to change there for the train which will get you to Southampton quickest.
