You do not seem to know Tamil Nadu history.. Kerala did not exist as such in Asokan's time. It was part of Tamil Nadu in the Cheran kingdom. People spoke Tamil at that timne.Ashoka indeed aimed for TN,Kerala and SL.But those kings already accepted superiority of Mauryan King and so blood shed avoid.
Tamil Nadu never accepted Mauryan superiority. Tamil kings lined their armies against Asokan at the northern perimeteter and Asokan turned back his army and went home without engaging in war.