If what you have is perceived to be finer, then it gets emulated
Mongols conquered much of Central Asia in early 13th cen. But the Ilkhanate Mongols hardly "mongolized" local culture. Rather they got persianized themselves
Nor are their merits and demerits
There's a reason Western ideas in 19th cen influenced Indian intelligentsia far more than Islamic ideas did in say 13th cen
So Indian thought was not greatly transformed
Whereas the encounter with the West ended in an intellectual setback. Thus transforming ideas more fundamentally
There is no doubt the story of India is one of Sanskritization
The idea of India / Bharat begins with the early Vedic settlements in North West India.
With likely the earliest state formation being the ancient Kuru state
The rest was likely wilderness. Not Aryanized yet.
The story of India in one sense is the "spread" of that culture across the rest of the subcontinent
And likely had covered much of the subcontinent by around 200-300 CE
What was not complete is the "vertical spread". Percolation of ideas down the social order
That process I guess continues to this day
And I think there is some merit to it
It is the story of the genesis of the idea of India.
Today it means a lot.
So that is sanskritization in one sense...the physical and intellectual colonization of Vedic culture starting from its core base in the "Brahmavarta" region
Until perhaps the 20th century - an alternative idea that grew out of the "nationalist" movement
One that attempts to position India as a new, culture-agnostic constitutional republic
Modern Indian politics is basically a conflict between these two ideas of India
And it must be said the former idea has made a great deal of concession to the latter