The term "India," the supra-regional entity, has been in use since millennia and there is hardly a manner in which it can be changed. Plus the term India has been derived from the term Indus (I may be wrong here). So it does have a certain amount of historic credibility.
The initial euphoria of nationalism during the British Raj did not call for a divided "India." They simply wanted British "India" to be changed to Independent India (comprising the many modern day nation states). The modern day India is seen as a continuation of "India" and everything "Indian;" I think this is justified. The creation of modern day Pakistan is seen as the partition of "India" and by many as the partition of India, as it (India) is a continuation of "India." This is where the confusion starts. This is solely because the idea of Pakistan took root much later than nationalism (India) in the subcontinent. Pakistan's history is a part of "India's" and to a certain extent India's.
There is no usurping of Pakistan's history. Pakistan's history is a part of "Indian" history. I honestly see no conflict. But perhaps I being an Indian, my views are not that unbiased and "real."
Yes, we would disagree on some of the points you raised.
Even Historians will not use the term "Indian" to describe the people of Pakistan, though the peoples/descendants of peoples in the lands comprising Pakistan have been around perhaps as long as any other people in South Asia. If in fact the
Human Migration Theory is correct, then the area comprising Pakistan would have been populated earlier than the areas further East in today's India, with the population eventually migrating and diffusing into India/Nepal/Sri Lanka/Bangladesh etc.
The name India,as has been pointed out, was also initially coined by the Greeks to primarily refer to the region comprising today's Pakistan.
Yet the association of the word "India" with the present political entity is so strong that it is not typically used for anything major related to anything but today's India.
There is a contradiction when we talk about a "region" called "India" (which you agreed to earlier), and then suggest that "the history of Pakistan is a part of India's" (in this context the only thing you could be referring to would be the current Indian State).
Since there was a larger region called "India" (called so not by the residents of South Asia, but rather foreign historians), then it only makes sense to argue that the history of today's India and Pakistan is a part of the history of "the Indian Subcontinent" or South Asia.
You could argue however that the history of Modern India is a part of Pakistan's history, and the history of Pakistan is a part of Modern India's history - and the histories of both are part of South Asian history.
Another point that causes some of this confusion is the suggestion that Modern India is a continuation of Ancient India. It is really only a continuation in name. No such entity existed historically.
Yes the historical cultures of ancient India have continued into Modern India, but they have also continued into Pakistan, and into Bangladesh, Nepal, Bhutan, Sri Lanka etc.
The history of all of these nations is a common South Asian history, and they are all a part of each others history. They are not part of "Modern India's" history alone.
Hence my argument that the history should be referred to as South Asian history to remove all this confusion and redundancy of names, and suspicion that Indians are fine with everyone else's history being a part of "modern India's history", but not with anyone else claiming the same.