I have never believed the broad assertion by some traditional authors and speakers that Sanskrit is the source of all Indian languages. Because I have a basic working knowledge of Sanskrit and very good understanding of Kannada, which is considered a Dravidian language, I have always felt that these languages are very different. Sanskrit is considered today as belonging to Indo-Aryan family of languages. Any similarity to Sanskrit, I explained away as an influence. This makes sense until we have doubt in very category these languages belong to.
All of us who studied some Sanskrit and even those who are familiar know the word arya does not refer to a community at all. There is no community by the name of dravida either! Then where do these names for language categories come from? I do not know. But when we start understanding the roots of several words, what is startling is, they do seem to originate in Sanskrit. Are these categories of languages correct then? I can not say.
I believed until recently that Kannada had nothing to do with Samskrutam. I defended this view for years. But as my understanding of Kannada and Samskrutam both increased, I started encountering research that showed both languages are related. Such understanding requires a very advanced understanding of languages hard even for native speakers unless they are native to both languages. It is not clear if the languages were related to pre Vedic period but the alpha-syllabic system is common. Grammar at a higher level is similar. Words are clearly common in most cases. This and research by others leads me to think the western classification of Dravidian languages is superficial. There is a chance that Samskrutam and Kannada etc are related very intimately. We do not know the exact nature of that relation. But it is likely a common language is the mother language of southern and northern languages.
Listen to the book review. It sheds some light on the issue.