Lyndon Johnson used a lie like that against his senatorial campaign opponent, in his first Senate run.
The charge was a blatant lie and everybody knew it, so he circulated it as a whispering campaign. Asked why he bothered circulating something so palpably false which the opponent would deny, he narrowed his nasty, pig eyes (typical DemonRat) and said, "I just want to hear him say it." He knew the power of a charge of pedophilia to unstarch voters' commitment to any candidate made the target of such a charge.
Robert Caro told that story in The Path to Power.
I’m not sure anyone’s mentioned this yet, but—
the thing with sexual abuse charges is that they are made anonymously. If they are minors, it is nearly impossible to cross examine them.
Such charges smear the defendant for life, and they are burdened with proving their innocence under the presumption of guilt. I guess perverse laws are required for perverse acts, but it is easy to see how quickly such exceptions can be exploited.