Does the easyJet flight take up two stands?
easyJet operates Geneva from a number of UK airports and nothing else. Even Birmingham only gets a couple of other destinations out of them - Belfast and Grenoble.
It was easyJet Switzerland and not easyJet that decided to fly into SOU. Their commercial teams are run almost at arms-length.
If I was SOU management I would also be a little hesitant to allow easyJet to compete with Flybe on too many of their services for fear of losing Flybe. easyJet isn't a perfect fit for SOU given operational limitations mentioned ad-nauseam.