Hoover held onto power for ~50 years in large part by maintaining files on the vices of politicians, public officials and celebrities. That experience taught him to be discrete about his own vices--and to let out just enough about them to keep the blackmailers at bay, the better for him to blackmail others. The idea that he'd let himself be photographed in drag is absurd.

Hoover didn't go after the Mob for two reasons. First, he was obsessed with the Communist Party USA, and he knew that he could always get Congress to appropriate more money to fight the "Red Menace," even though it practically disappeared after WWII. What Senator or Representative would go on record as opposing more money for the FBI to fight the "Red Menace"?

Second, Hoover often said that if local and state law enforcement did their jobs, the rackets associated with organized crime would disappear in weeks. He wasn't wrong. The other side of that statement was that he knew how Mob money could corrupt any and all law enforcement.