Stealth,
A slight digression, but the questions you raise in your first point are exactly the questions raised to debunk the idea of modern India being a continuation of ancient India, in terms of ancient India being any sort of unified entity.
Who said that Ancient India was a unified political entity. It was a unified cultural entity, as compared and contrasted with other cultural entities.
But back to the topic, the question of whether the IVC were city states rather than a single empire is moot because the argument is that empire or city states, they existed in modern day Pakistan.
They existed in an ancient cultural entity called "Ancient India", not in the modern political entity called "Pakistan"
As to what happened - the most plausible theory is probably that like the Mayan and Aztec City States, they made very tantalizing targets, and their breakdown probably resulted in the IVC people moving into smaller settlements in the surrounding areas.
There are several theories, including ones which say that climate change forced the tribes to move eastwards well before the arrival of the new races.
Even if they were wiped out completely, the fact that the majority of the civilization was present in Pakistan gives Pakistan the right to claim it as their history. We are after all not going to tell the Greeks that their ancient history is not theirs just because they cannot explain every single event and attribute associated with it.
But the Greeks are by and large descendants of the Ancient Greeks. The same cannot be said about modern Pakistanis. Perhaps, a small fraction of them, but that's all.
Even the American settlers mixed with the Natives to some extent. That doesn't make American settlers the inheritors of the histories of the native tribes.
If the people migrated, and their customs and way of life evolved as they interacted and mixed with other peoples, then they were not the IVC any more were they?
Yes, but this would be a positive assimilation rather than a diminishing one or nonexistent one.
Who knows, the modern day IVC people could be identified as an isolated tribe in India, but the same can be definitely ruled out for Pakistan, because the gene pool has been almost completely replaced.
One definition of civilization is "the type of culture and society developed by a particular nation or region or in a particular epoch".
If migration (out of Pakistan or merely out of their cities) was the cause of their disappearance, then I would argue that they did not meet the requirements of a civilization any more, but that still does not diminish the fact that as a civilization they lived and prospered in the lands of modern Pakistan primarily.
Once the civilization itself ceased to exist, shreds of the culture, customs and knowledge would still be passed onto the ancestors of modern Pakistanis through the remnants of the IVC, and hence Pakistan's claim to that history.
You are simply giving more importance to the "Land" part of a civilization than the "People" part in order to bolster your argument.
Why should the land be given more importance than the people?
Besides, the modern day Indians have inherited far more from the Harappans in terms of culture than modern day Pakistanis have.
On a different note, many Indians are incensed by the fact that on one hand, Pakistan has sought to dissociate itself from the subcontinent by claiming to be a Central Asian/Persian/Arab culture, and on the other hand, it tries to bolster this seclusion by claiming that even its ancient history is completely different from India.
