Though there were periodic intrusions of South Asia from the west, there seems to have been little flow of people and political power projection from South Asia out to Iran and Turan.* Why? Traditionally I have favored geographically contingent parameters. Populations from warmer climes tend not be well prepared for the winters in northern climes, while those from frigid climes can usually adapt by shedding clothing. The difficulties of the Arabs in pushing their power very far north of the Caucasus was an instance of this, as the records seem to indicate some difficultly in adapting to the reality of the north Eurasian winter (Islam’s penetration of the north came via the conversion of the Turks). In contrast, Turkic peoples have moved south for the past 1,000 years with relative ease.
But I realized another factor which I think is more important in hindsight: pre-modern elites were generally in the business of extracting rents from subjects. The more subjects, the more rents. So, the ruler of India is clearly far wealthier than the ruler of Mongolia, even if the average Mongol has a higher per capita level of wealth and health. On the margin there simply wasn’t much profit in conquering wastelands for autocrats of densely populated regions. This is clear in the historical record, by the time of Claudius it was presumed that his conquest of Britain was more a matter of personal vanity, glory and prestige, than necessity. Though particularly egomaniacal potentates, such as Han Wuti, may have felt that there was a need to send massive armies to conquer lands which were barely inhabited by savages, in general these societies felt it more rational to simply pay off the barbarians outside the gates (the Chinese case is well attested, but the East Roman Empire did this for centuries leading up to, and after, the fall of the West Roman Empire).
It is clear from the early Muslim annals that India was viewed as a land of riches. But, I think we misunderstand the perspective if we view India as the Netherlands or Japan of its era in relation to the Mashriq or Iran. Before the Industrial Revolution the average standard of living in all societies was only marginally above subsistence. Differences of per capita wealth were on the order of 10-20%, or less. Not the multiples, or even orders of magnitude, which we’re familiar with today. So how was India so rich? It was rich in people, so from the perspective of predatory elites it was a place where you could become very rich indeed.
The best analogy for wealth then is how some African pastoralists view their cattle. More cattle = more wealth. More subjects = more wealth. Not because individual subjects were wealthy, but because stealing a small amount from more people sums up into a large pile of rents extracted. Of course such economic-structural arguments have their limits. The Mughals periodically attempted to conquer Samarkand. Why? Because they were Timurids, and Samarkand was the traditional seat of their lineage. In other words, there are emotional reasons to conquer worthless territory which does not redound to one’s bottom line. That certainly explains much of 19th century European colonialism, which was on the balance a transfer of payments from the citizenry to the well-connected aristocrats and plutocrats, who could take advantage of opportunities offered in the colonies.
* I make a distinction here between demographically salient events, such as mass migrations, and culturally influential ones. In the latter case obviously Buddhism, and to a lesser extent Hinduism in Afghanistan, flowed to the northwest.