If Cain sues for defamation, he will be the plaintiff and will bear the burden of proof to show that it is more likely than not that these women intentionally, knowingly, or recklessly made false statements to injure his reputation. 14 years after the fact, he will have a difficult case carrying that burden of proof. Additionally, the court cases would take 22 months on average. And if he loses even one suit, that would be misunderstood by the public to mean that what the sleazebag said was true.
Bieber’s case was perfect because his dumbass accuser made a statement that could absolutely be proved true or false. Believe it or not, there might still be some issues with intent, but he can definitely prove it false. Cain can’t because the claims were so vague that there’s very little to get the hooks in.
This is less about suing for damages, than it is about public opinion. Your last point about intent is correct: Cain only needs to prove it false.
The very mention of a courthouse would create pressure for the women to throw their cards on the table. Their refusal to do so, would of course favor Cain. I’m not so sure about the 3rd lady: 13 years is a long time.