I want to read about a story where a villainess actually remains villainous after rebirth. Maybe she wants to usurp the throne and start an empire, instead of just trying to "survive" the original plot.
My personal interpretation of that "If You Kill Him, You Become Him" trope is that the Heroes are not killing the villain because it's not their job. If the story were in a war setting and the villain is on the opposing side of the war, then by all means kill him. Otherwise, if they kill him...