Gordon Liddy answered this question 35-odd years ago. When a train’s in trouble and the engineer’s dead, the crew and the passengers don’t need a civil or chemical or nuclear engineer, a lawyer, a doctor, a carpenter, or a good person or a nice guy; they need a railroad engineer, someone who knows how to right the train. It’s only after they’ve found a few railroad engineers that they’d have the luxury of weighing the candidates’ other assets and liabilities.
Despite his resume, Cain doesn’t appear to be that engineer. And without that qualification, the liabilities—whether true or not—don’t matter.
Oh, I’ve heard that argument before, and it certainly has some merit. But I still separate the role of “leader” as something beyond what an expert craftsman, engineer or some such does. There’s a moral component to leadership, which I can’t discount.