Mughal civilization instead of Indian? Seriously? Mughals were an important, but ultimately, only one portion of the long-lasting Indian civilization. Indian history does not begin and end with the Mauryas, Mughals and Gandhi. There have been many other great kingdoms and kings; they just didn't rule over as much of India as Ashoka or Akbar did.
Also, why would you prefer Shah Jahan over Akbar? Shah Jahan isn't comparable to Akbar in stature.
Why should it be the Mughals in all civ games:
For the same reason that it's Rome, and not Italy.
The Mughals are the best known, and one of the largest and most influential of Indians various nations. While the Maurya and Gupta could also make a run for the position, outside of India,how many people could tell you where those civilizations were, or even that they were Indian? Then find out how many of them can name a leader (besides Ashoka) of either of those two civs. Rather than using the name that we know the area as now, they should use the name of the actual great civilizations that have sprung up there. India, like Italy, spent the vast majority of history being only a geographical term for a spit of land, not the name of a nation.
Modern India is even worse. It's major accomplishments include: tying in war against a country several times smaller than it; and creating a spin-off of Hollywood.
Why shoud it be the Mughals in Civ5 specifically?
because both the Mughal Fort, and the Mughal Elephant are the unique units. Why not just go ahead and make the civilization the same one you took it's UU and UB from?
Why Shah Jehan?
I like him better personally. He's got a cool name. I personally don't care which Mughal Emperor was used, as long as they were to finally stop putting someone who NEVER LED INDIA in charge of India. Personally, given the strong advantage given to warfare in Civ5, it should probably be Aurangzeb that leads. If they went with the biggest and best leaders, Hadrian would probably lead Rome (he died shortly before what is thought of as the "high point" of the Roman Empire, in AD 150, and is much better known than Antoninus Pius, who was the actual emperor at that point)
TL;DR: I could care less if it was a Mauryan, Guptan, or Mughal civilization in Civ, as long as they stop pretending that the nation of "India" is or has ever been, anything more than a regional power, and as long as they stop claiming that Gandhi was a president of India. I choose the Mughals as my choice based on the UU and UB in Civ5, and my choice of leader for the Mughals was a simple matter of thinking Shah Jahan was the coolest of the emperors.