Kavanaugh is a public figure, as such, it is extremely difficult to prove libel or slander *with malice aforethought* which is the bar set for public figures. IOW, you not only prove that it was a lie, you have to prove the accusers knew it was a lie and that the accusers did so anyway with the intention of doing harm to the accused.
A SCOTUS justice, if anyone, already knows this and would be stupid to sue. If this gets to impeachment in the Senate then, by all means, produce a defense. However, suing to clear one’s name in this case is as stupid as making a murder defendant take the stand in their own defense. There’s a reason lawyers counsel their clients not to do it.
Isn’t the fact the charges are being made forty years later, with no corroboration, prima facie evidence of malice aforethought? Why else would they be doing it?
Balsey Ford’s lawyer let it slip the purpose for making her charge was to put an asterisk next to his name. In other words, to dirty his reputation.