Here's the funny thing about "extermination campaigns": Mostly they cause whatever "pest" you are trying to eliminate to grow improbably strong and "badass". Have you watched what happened after antibiotics were invented? The microbes have evolved so fast that we are on the verge of not having any that can be used in "last resort" situations. How about our use of pesticides? Ever heard of " super lice"?
Bottom line: The intended victims of extermination often end up stronger in the end. God wins.