To their credit, Southeastern will declassify the first-class sections when the train is crowded. Nearly every morning I've heard the driver or conductor announce that they are doing so, and inviting people who hold first-class tickets to apply for a refund. By the time I hear the announcement I'm usually settled on the floor so I don't bother to move, but do they not do the same for South Western?
But to be honest, I have no idea why you'd buy a first class ticket anyway. The seats are no different to standard class at all, apart from a thing on the head rest saying "1st Class". They're no wider, have no more legroom, and all the standard class seats have the same tables and armrests. Literally the only thing I can think of is being guaranteed a seat - but given that I rarely see a conductor enforcing tickets for first class passengers, and I doubt very much one passenger would challenge another, there's nothing to stop me just sitting in a first class seat on a normal ticket.