The fact that entire region was called Bharat escapes you I think. Just before British India was centrally organized and ruled by Mughals and Marathas so your argument does not stand.
As far as "divide and rule" is concerned, due to the vastness of India regional leadership was always delegated. British utilized this structure to their advantage.
I don't think that important fact inherently implies a unity that was never there. The(roughly defined) region called "Europe" has never been under the control of a unitary state or empire, even in the times of the Romans.
https://en.wikipedia.org/wiki/Roman_Empire#/media/File:Roman...
Delegation is not the same as "divide and rule". There was active animosity amongst these provinces. The British played Bengal and Punjab against each other, for example. The Marathas did resist the British in their own strongholds, but they never centrally ruled an undivided India. It was a big empire nonetheless.
There was a concept of a united India/Hindustan/Bharat/Aryavart in Ancient times.
The Marathas never controlled an "undivided India" given the extent of their empire at it's peak: https://www.mapsofindia.com/history/maratha-empire.html
Not to mention, even Akbar did not have the North east and the southernmost parts of India.
The rise of the Sikh empire, and the Deccan sultanate also limited the extent of the later Mughal and Maratha kingdoms.
I did not question that these empires had their time. But the notion of undivided India as united as one under the Mughals at the time right before the British arrived is wrong. Ancient times do not affect contemporary affairs, or in this case affairs of 1750s are not affected by the Maurya dynasty's claim on some version of modern day India/Pakistan/Bangladesh.
Video: https://youtu.be/QN41DJLQmPk?t=628 (at 10:28).
Some other interesting time lines from a union of India perspective from this video:
Maurya Empire: 270 BCE (at 2:01, https://youtu.be/QN41DJLQmPk?t=122)
Delhi Sultanate: 1344 (at 8:44 https://youtu.be/QN41DJLQmPk?t=524)
Edit: Found another video that matches with the above video regarding Mughal Empire: https://youtu.be/wYu2jyVTSc8?t=76 (at 1:16).
The peaks were quite short-lived, often only one ruler's lifespan (natural or otherwise). There were long gaps between. There were many competing powers.
And that's OK! I mean, are we sure that the world in which some Aurangzeb figure won, and created a united (persian-speaking, 100% sunni) subcontinent, is a better place?
This is a huge simplification of the history of the Indian subcontinent. The British are the architects of the new boundary lines, but they are also the architects of what is now a unified country, India. Indian subcontinent as a unified entity prior to the arrival of the British as a major colonizing force in India is a lie. India was quite divided before that, which made it easy for them to play their little game of "divide and rule".
None of this absolves them of responsibility, but this over-simplified statement irks me, as it is a gross misrepresentation of the politics of the Indian subcontinent prior to the British.