"Southwest, the airline based in Dallas, Texas, which has been the model for both Ryanair and Easyjet, has gradually eaten into the dominance of the American giants and won almost every head-to-head battle against them. It is now America’s fourth-largest airline, carrying more than 70m passengers a year. "
What?
There are no "head-to-head" battles, except with bus companies. SWA excels at bypassing crowded hubs and providing point-to-point service for the "flyover" country bypassed by mainline carriers.
When in directly in competition with said carriers, all ticket prices quickly become comparable. For example, I can fly KBHM-Baltimore for ~$200 on Delta, whereas KATL-Baltimore (a non-SWA route) is closer to $500.
To simply state that SWA excels due to lower costs is ignoring the true genius of their route structure. They "hit 'em where they ain't."