Colin, you've long been one of my favorites on AZB, but I don't think this comparison is fair. Yours is an argument of pure economic theory, and seems air-tight on the surface.
Still, I think you'd agree that opening a dry cleaner next door to one that already exists and intentionally operating at a loss in the short-term may not advance the interests of anybody. The result is that the established dry cleaner goes out of business and the new one must then greatly increase its prices to avoid extinction. Once it does, it, too, goes out of business. Nobody wins, and the more cost-efficient provider of service has been eliminated. This story isn't one of good clean pure competition, but one of destructive business practice. Throat cutting just for the sake of it, with the result being an unnecessary and undesirable reduction in supply of something desired in the economy.
Pool has a few too many stories in its history that make me think of the dry cleaner story rather than the Burger King story.
PS Dry cleaning as a business was chosen at random, and the hypothetical story says nothing about my feelings on a sector of the economy which I know nothing about.