Your understanding of history is quite flawed, for the simple reason that you seem to be comparing historical empires with modern federal states.
Yeah, like the Yugoslavian empire, the Czechoslovakian empire, the Romanian empire .
The point of mentioning the empires is because they were the largest political units and have now ended up in dozens of smaller nation states based on ethnic homelands. I could have started at any stage of the gradual deterioration of impractical national units down to its current form.
If anything, you should be comparing India and Pakistan with countries like the US which have created a successful federation based upon democracy.
Not only is the US not any ethnic groups homeland (minus the natives who are effectively powerless and disorganized at this point in time) but one of the fundamental concepts of the US is immigration.
It is a completely different situation.
Obviously, multinational empires would tend to fall apart because they are comprised of one dominant ethnicity or nationality subjugating a number of weaker ones. This model is not applicable to India because everybody gets a stake in the national interest and no ethnic group dominates the politics in the country.
You just described exactly what the British did throughout its empire (including India) for most of the past 400 years. If you think India is somehow different you are mistaken.
If you aren't even unified on language (referring to the official state-level languages and how varied it is in India) you can forget about cultural unification - Bolllywood will only take you so far. Even Canada came to within 1% of a referendum vote to have Quebec separate. Canada is a modern, prosperous and democratic state light years ahead of India and the language barrier brought it to the brink of independence. The only thing that prevents this is the greed - the Canadian government disproportionately funnels money into Quebec to keep their separatism under wraps.
It's in India's interest to have a Pakistan/China boogeyman until it brings prosperity to the majority of its citizens. As sad as it may be, greed and fear have been the underlying factors of unifying diverse ethnic and cultural groups and that is no different for India than any other nation today, including my own.