Even if you go to Gatwick in the middle of the night (2am - 4am) the trains are not at all busy. There might be a case for early and late trains on some routes but people need to feel safe on them.
How busy are the Thameslink trains?
I can't see 24 hour railways coming to South Western Railway. There are mutiple routes or 4 tracck to get to some of the places, e. g., Surbtion, Woking, Guildford and Basingstoke but I don't see it happening even with this.
I mean the only time a 0:50 Waterloo to Portsmouth service is run is on Monday mornings for the Royal navy. Nothing on Friday or Saturday night when non naval personnel might be out in London. If they don't see a need for a late service other nights, no chance of 24 hour running.
There use to be overnight coaches on the, North Downs Line and I was once on one of them. However they stopped, no doubt due to not being popular enough.