BUT - the reason Southwest was the "low fare" leader was because they locked in fuel prices back before we had the massive spike in prices in the early 2000s. That gave them a tremendous advantage over the other airlines given fuel is such a massive part of their overall costs. That combined with standardizing on a single plane (less impactful but still helpful) allowed them to both claim and honor the "low-cost leader" title.
Now that fuel prices have returned to a more "normal" state, their prices had to revert to the mean. They may be cheaper on some legs, but it's not universal anymore.