For most of history, Turkic languages were not looked upon as prestigious or worthwhile. Most (perhaps all, though there may be exceptions) of the states of Turkic origin in the eastern half of the Muslim world used Persian as the language of court and intellectual life, for instance the Mughals and Safavids. In the Ottoman Empire, Turkish only achieved prestige starting from the sixteenth century. The Arab lands which were under Ottoman rule received some degree of linguistic influence, with some words entering colloquial dialects.

But leaving all that aside, the main answer to your question is that Turkic rulers were not generally interested in culturally assimilating their subjects. There was no Ottoman effort, in the early modern period, to encourage common people to speak Turkish. Nor is there any particular reason why they should have done that.

Anatolia's adoption of the Turkish language was closely linked to its conversion to Islam - as the local population became Muslim, they joined the growing Muslim community which already existed there and learned its language, which was Turkish. Because the process of conversion was gradual, the converts assimilated rather than forming new communities with their local languages.

From an Indian perspective, modern north Indian languages have quite a few loan words that are of Turkic origin. The most prominent example is the word Urdu itself, which originates from Ordos, the Turkic word for an army camp.

I am not aware of Turkish rule in India/Bengal, are you referring to the Mughals? From what I understand they weren't turkish.