Geopolitics, geopolitics! Rome played the divide and conquer route so expertly I am sure Britain in history class was like "WRITE THAT DOWN! WRITE THAT DOWN!"If China, Iran and Rome could unify, why not India ?
Persia, is much more complex, shared identity, yet different culture, intrigue, alliances, unions etc.
China was virtually united after the Yangtze River Civilization anyways so that was moot point; they had no racial differences yet were divided for a long time as well fracturing, that paints how geo-politics works, because even states that speak the same language (not like diverse india), share the same race (not like Burmese/Indo-Aryan/Dravidian India) could be fractured so many times, it goes without saying, unifying India is going to be very very very hard.