Search Twitter for the Pence Rule and you'll find that most tweets are critical, and more assume it's a rule against temptation, rather like Ulysses having himself bound to the mast so he could safely view the Sirens.
I don't know Pence's original explanation of his rule, but it strikes me there's another interpretation: as a defense against misleading appearances and false allegations.
The usual interpretation in effect deprecates men as weak-willed and passion-ridden figures; the alternative view deprecates women and the general public as prone to lies and to believing lies. Why can't both be true? I don't know if Pence is Calvinist, but it sounds like the Pence Rule is.
Of course, as said in The African Queen, we're supposed to rise above our nature.