> Most of their travel traffic is from the leisure segment anyway, so them not getting business traffic isn't the end of the world

This. Southwest (and the other LCCs) can't really compete with the 'kickbacks' provided by traditional carriers. If you're responsible for a lot of corporate travel, or you do a lot of corporate travel yourself, carriers like AA effectively make it so you never have to buy a personal ticket, and get upgraded to a higher level of service on many of your flights.