Financial services tried the India experiment. Some of them had to bring the jobs back, because customers complained of the language barrier (we speak English differently) and the cultural barrier (inability to understand that the customer is right).
On the other hand, tech jobs can be successful. For example, the night crew for Oracle is in India and they are really good.
Not only that, you need a Series 7 license to perform many of these functions. I don't know if it's possible for Indian nationals living in India to get one.