There is a great business case for extending the runway at Southampton. It's been in the region of 2M pax and just before that in 2019, that's based on a limited route network operated by Dash8 and a token presence of a low cost jet operator.
Just taking a look at key towns/cities close by we are looking at 1million people. Gatwick is 87 miles away and Bristol just over 100. Let's not forget it's possible that a, meaningful operation could draw users from South London and the surrounding counties.
The cruise business will recover, this drives significant volume into SOU, the port also generates traffic.
If I were running SOU, post expansion (not discounting the challenges of expansion) I'd be aiming for 5M pax plus, a presence by a low cost airline, I'd not rule out Wizz and the likes of Jet2, would make a lot of sense.