28% of Indian students are enrolled in higher education. The gender split is 52:48 in favor of males.[1] For the US those numbers are 39% and 45:55 (more women than men).[2] Since they're from different sources the participation rates might not be directly comparable shrug but the gender stats should still be applicable.
At least going by that, there doesn't appear to be a great deal of "lock your girls and women away" going on over in India.
The upper classes in India are a rounding error, maybe the population of Spain at most.
Edit: you are right that it's a trade-off. In Bangladesh keeping women at home may mean starvation, so they are grudgingly allowed to work.