the average American will only personally encounter "family-business" Indians running convenience stores like Apu from the Simpsons or hotels like many Patels. Average Joes don't usually read political commentary or anything intellectual (much like the average Indians dion't read because of illiteracy), instead relying on some cable or talk radio show to tell them how to vote.
India might have done better without the sectarianism that led to partition and ongoing communal violence. But historically few nations have practiced government secularism to the degree that China has.
I would prefer to neither be the hated giant (China isn't even a giant yet, with limited military capability, why be as hated as the US?) nor the caged bird. Rather, it would be better to simply not be noticed while US attention is focused elsewhere.
Americans have been turning against India in recent years. I think the elites (who, contrary to your assertion, depend on popular support more than they themselves know) probably think India will remain stuck in its current rut permanently so don't consider it a threat in the long term. They could very well be wrong.