It will be interesting to see the results of this if we even get to see them. It's not an accident in the official sense and I don't know how much of the investigation would be made public. Certainly civil lawsuits are likely and SWA has to be prepared to defend those.
It's very possible the airline will not fire the pilots as long as they didn't do anything blatantly outside of SOPs or negligently disregard SOPs. Still, one wonders how it's possible to do this and still have followed SOP. It's possible there will be some question that the airline's procedures need tweaking and they probably will be.
Many years ago an ATR landed at the wrong airport up in Wisconsin? (going from memory here)...I think it was destined for Appleton and landed at Oshkosh? In that case the pilots ended up in serious trouble not so much because of the wrong airfield but because of what they did after....told some lie to the passengers and then took off and again (without a dispatch release) in order to proceed to the correct airport.
I wonder at what point the crew of this SW flight discovered the mistake and what kind of words were said. I'll bet it was one hell of a moment of realization. It's how they behaved after this moment I think that truly defines their character and professionalism. We all make mistakes, we just hope they aren't big ones like this.