I'd say a population of around 10,000 is about the threshold for an own railway line. For example I can see that, if it was not on the main line to Salisbury, Romsey (pop. around 15,000) would probably support its own branch.
However I do recognise that Swanage has an unusual geography which means that it's a long way round to get to Bournemouth or Poole and that might limit the usage of a regular daytime commuter/shopping style service.
Swanage is an easy daytrip destination for the Solent area, certainly, at least by car (despite the regular delays on the A351). A rail journey would actually end up being quicker than the car from, say, Southampton, as you wouldn't have to battle with the Bournemouth-Poole suburban roads and their heavy traffic, nor the A351 north of Wareham. And arguably Purbeck is doable as a daytrip from the London area too - so I can see a regular service could work if the connections off London services were good.
And besides Corfe and Swanage themselves you get access to the coastal scenery, and some exceptionally good walking routes.
If there was a good bus network (in the summer) and a cheap weekend bus/train ticket, with a bus linking say Swanage, Corfe and Lulworth (would have to probably go via Wareham) I can see that could work for the weekend trip market. Train down there, then use the bus to get around during your stay, or train to get into Bournemouth.