Loganair and Eastern are the only long term survivors in the UK regional airline sector, the latter arguably only because it is bank rolled. Everyone else has either gone bust or pulled - out the best example of the latter is BA, who gave up on it years ago. For some, (EasyJet) the UK domestic market is a very small part of the overall operation.
Loganair have survived by being very conservative- they will never over supply, they will just make a decent yield and offer a frequency on which they can sustain that probably around 2 -3 flights per day. They can always retreat to Bonnie Scotland and the subsidies available there.
Without any prospect of PSO routes Southampton will have to survive - by attracting airlines -as Teesside has arguably done or relying on operators believing they can make money. _ it's no good begging to airlines to come and do more.