Speaking to some people from India, and my own readings what combined their society was a couple of things : a deep connection to the traditions such as the vedas, sanskrit, gods, brahmanism. And even if there was divergence, it was usually with a deep respect for what had gone before. So surely while there was a lot of cultural divergence, there was also a lot of things that made it into the India we see today. Some empires also endured a long time to make more of cultural unity. I am not sure in how far Bharat was used for the whole subcontinent and where.