It wasn't part of Khan's character (the "genocidal madman" thing was an innovation of STID)...
Actually, I'd say the potential to be a genocidal madman goes to Greg Cox in his Eugenics Wars duology. Where Khan has the "Morningstar" weapon that was capable of wiping out life on Earth, IIRC.
Orci and Kurtzman have pointed to the novels as inspiration for the work they've done. Mr. Cox novel may have been part of the reason they developed Khan the way they did.