Who would US protect India from? And who would US protect China from? Just ask the question and you have the answer.
You only need to look at history, if you want answers.
China ran to US for protection, twice... (protection from japs in 1937-45, when eventually US got china liberated in 1945. Then, protection from soviets in 1970..).
India has always been on its own since bronze age civilisations... leave alone the issue of USA or even any other party being involved in britain's peaceful exit from India in 1947.