The trouble with that is that (leaving aside some operational considerations), SOU is usually going to be more appealing, due to:
- it's existing network of domestic & near-european routes
- a main line railway station outside the terminal, which can convey you to London in around an hour (or Reading, Basingtoke, Oxford, Birmingham etc. without a change of train)
- a adjacent Motorway, again feeding London, the Midlands as well as the south coast (east and west)
As others have said, the niche for BOH is serving the routes/markets that SOU can't, eg, mid-haul charter and lo-co.