Tamil is a classical language like greek, hebrew, chinese etc. Its much older than telugu and the other Indian languages. Malayalam and kanada is derived from tamil
Of course Kannada evolved from ancient Tamil. If you know both the languages, you can easily find root words for most current day Kannada words in ancient Tamil sangam poetry (like ooru=>oor referring to town, kaaveri=>kaaviri, etc.) https://en.wikipedia.org/wiki/Dravidian_languages
Kannada, Telugu, Malayalam all have higher degrees of impact due to Sanskrit but they are all dravidian languages, derived from ancient Tamil.
Your Wikipedia link disagrees that all of the Dravidian languages are derived from ancient Tamil. It describes them as common descendents of Proto-Dravidian. It cites the attested literature of Tamil as being 2,000 years old.
The Tamil language currently used is not same as the one when the other Dravidian languages separated, So calling other languages 'derived' from the Tamil is not correct. All Dravidian languages have same root, so calling it 'Dravidian Language' and Tamil, Kannada, Malayalam & Telugu etc. derived from that language is more accurate and avoids the confusion
> an enormous literary corpus reaching back to before English even existed
Certainly true of Telegu, Tamil, Kannada, and Malayalam. But because Bengali is, like English, an Indo-European language, not true of it. Also, not sure what you mean by "etc".