In many markets, Southwest has not had the lowest prices on average for a long time. They may have a lower price here or there, but they benefit from not publishing their prices to OTAs and thus it being cumbersome to compare prices every time (so many people probably don't bother and thus assume erroneously that Southwest has low prices). And their low-fare summary is useless if you only want to fly at certain times of day, because the lowest-fare flight of a day is typically something very early in the morning or very late at night, but that's the only price you can see in lousy summary.

A lot of people hear about Southwest being called a "low-cost carrier" and don't understand that the term LCC has nothing to do with fares, and only has to do with operating costs. And thus, because they can't see Southwest fares side-by-side with any other fares anywhere they look, they continue in the illusion that Southwest is low-fare airline.

Southwest pluses are in most cases not their fares, but their policies (no charge for the first bag, no fee for changing a flight (just pay the difference in fares), no fee for cancelling a flight, etc. Of course for those who carry-on only, and rarely change or cancel flights, that may not matter that much.