Why would a private company be interested in running that service which would clearly be very loss making though? For example, I can't see why they would have a single passenger on the Redbridge to Bournemouth part of the journey.
Reading my post again using the words: "may run at a loss to start with" was a poor choice of words.
What I was trying to say was that the trains may not be full and standing from day one and it would not be ideal that to get to/from Southampton you would have to change at Redbridge but if the timetable could be done so you are waiting a maximum of ten minute's then it should be fairly acceptable to a decent amount of people and while I agree it is unlikely you would have somebody daily commuting Redbridge - Bournemouth, as Dougal2345 #193 points out if you have stops at other places "it would be quite useful" not only for people who already make journeys but people who might now, for example, look for work in places they may not have done before because of no/bad transport.
But only to Bournemouth, not to Southampton. And if these stations would be profitable with 2tph, surely SWR would provide additional services.
While Go - Op has been stumbling from one disaster to another, a point that they made when they first proposed their service and I have seen elsewhere is the train service is very poor at Westbury, Frome, Castle Cary etc and that's because GWR has no competition so can get away with running a poor "Take it or leave it service" so by Go - Op running their own service's it would have forced GWR to improve their service.
And it is the same for this idea that if South Western railway had competition they would offer a better service so it would benefit passengers.
Really though the main aim is opening up the golden goose which is Swanage because not only would it mean commuters, students and shoppers could get out of Swanage easily but day visitors/holidays makers (via X - Country connecting at Bournemouth) can get in.
I don't think this is practical to do without impacting on the available length for freight.
Looking at Google maps there looks like two tracks running South of Redbridge station so one for passenger and one for freight.
AIUI the Swanage Railway trialled it's service and it wasn't particularly successful, to put it mildly.
The service started mid morning and finished mid afternoon so was useless for residents wanting too get out and day visitors wanting to get in it was also stupidly expensive.
Have a look at how Go-Op's proposals have gone for why no OAO is likely to follow that model.
That's the point, if they had followed that model then it would have stood a lot better chance of working.