We've got a few theories / analyses about this whole thing.
Theory #1: The Dichotomy of the Beauty Pageant: Why are these young women supposed to look sexy but not be sexual? They are expected to parade around in pageant-approved swim suits, but get blackmailed with pictures that reveal a lot less skin. Are beauty pageants the ultimate state of control over women and their sexuality? We get to dictate what they wear, how they walk, what questions they answer. Even slight deviation from this script has serious repercussions, threatening to remove the women from the pageant. Oh wait, does this sound like American society?
Theory #2: The Victim Theory: Being sexy and/or a victim are the only ways that young women can attract attention. When was the last time you saw a breaking headline "Miss California Receives Prestigious Mellon Award" or "Miss Texas: Class Valedictorian"? And yet a combination of blackmailing and a hint of inappropriateness has immediately put Amy Polumbo on top of Google searches and headlines. Clearly, we value good drama and sex over brains and achievement.
Theory #3: The Conspiracy Theory: Is Amy Polumbo just really smart in recognizing the potential of Theory #2? After all, these pictures are rather tame, so she either has one of the stupidest blackmailers in the universe or one of the smartest publicists. Playing victimized debutante has gotten her national media attention, landing spots on various talk shows. More power to her for working the script!