I think Southwest has proven this not to be the case. Their fares are consistently lower than the majors in spite of having no bag fees and their bottom line sure doesn't seem to be hurting any.

You could argue that the level of service isn't commensurate with what you'd get on a Delta or AA so its not the same product - but I'd say personally that my experiences with Southwest are far more pleasant than my dealings with any of the others.

edit: s/fare/far (pun notwithstanding)