The Tamil speakers have had a tremendous influence on World history because this group spread into Europe, India, Central Asia on into China and Japan. It appears that the first waves of Dravidian speakers (especially Tamil) went to Asia in search of metals which they exported back to Middle Africa.
The Tamil history is interesting because while one group separated from the main body in the Indus Valley to settle much of South India, another group migrated into China and founded the Shang Dynasty. These Tamil speakers were forced out of China, through Yunnan, across Southeast Asia and through Tibet back into India. This explains the influence of Dravidian (Tamil) on so many languages in Europe and Asia, including the Islands of the Pacific and Indian Oceans.
Once you recognize the history of the Tamil in Anatolia, as represented by the Kassites, and the fact that the Hattic, Hurrian and Kaska people also belonged the C-Group (or Kushite) people who left Nubia in search of metals after 3500 BC explains why Dravidian languages are at the base of Sanskrit and the Pakrits. Although the original "Aryans" spoke languages related to the Dravidian group when they entered India they came to settle new lands in where the majority of the population lived in city-states instead of an Empire with a central administration.
The Hattic, Kaska and Kassite people desperate for land because the Hittites, the first Indo-European speakers had forced them from Anatolia sent these nationalities eastward in search of new lands. Under the Elamites and original Persians these nomadic people were unable to establish themselves in Iran, except among the hunter-gather groups which may have been composed of the Proto-Indo-Iranian speakers.The Anatolians probably intermarried with Iranian speakers and probably adopted many Elamite/Old Persian terms, and like the Elamite/ Old Persians used the term Arya to denote their Anatolian heritage as rulers and elits.
Consequently, when the Aryans (Kassite, Hurrian, Hattic,and Iranians) probably entered India and found much of the authority situated in city-states (walled villages) the Aryans (Kassites, Hattic, Hurrian and Iranian speakers) were able to concentrate their forces and easily overthrow the Dravidian City-States and thus conqueror the North. The nomadic nature of these Aryans and led to their lost of the polish and sofhistication they manifested when they were the rulers of Anatolia.
As a result, there were probably numerous attempts of the Vedic people to return to Anatolia and recapture their heritage. But over time Europeans and Gutians took control of the region and they were forced make India the center of their culture and civilization.
If this is an accurate account of the origin and spread of the Indo-Iranian people to India, it would appear that the Indo-Iranian people would have remained a significant minority in India if not for the fact the India they entered was made up of City-States , instead of an Empire with a centralized polity and military.