I'm wary of relying on economists to assess the utility of the FDA. The alternative to the FDA they mention is basically self-policing. Except we already have a drug-like industry that relies entirely on self-policing: the "health supplements" industry, which the FDA is explicitly banned by legislation from regulating. And the precedent of the health supplements industry is extremely disconcerting--companies are basically legally lying through their teeth (it's not illegal if someone else, e.g., Dr. Oz, says it, cause they aren't advertising, they're exercising free speech), and they sometimes don't even bother to stuff their products with what they say the active ingredient is.

The problem with drugs is the placebo effect. Evidencing efficacy beyond the placebo effect requires large, controlled trials (the infamous Phase III clinical trial) that end up being correspondingly expensive; nothing less is sufficiently powerful. Because of placebos, you can sell expensive nothings, and it will appear to work sufficiently well that reputation wouldn't suffer.