I've been watching those programs as well. My mother was brought up in India when her father was posted there in Jan 1921 to be part of The British Army in India, she had fond memories of growing up there (they returned in 1932).
Its a familiar story. While there is stability (i.e. under British Rule) people get on with their lives peacefully, though there was the occasional sectarian killing I believe.
But when there is disruption, as in Partition, then the old Tribal conflicts come to the fore. The British didn't push for independence and certainly didn't want to split the country along religious grounds - that came from those wanting to take over the country and run it for themselves. The troubles started before the new boundaries had been decided. If it had been done over a longer timescale with people having what . . six months notice?? . . would it have been different. Somehow I don't think so. The only difference would be that the killings would have happened under British rule instead of mainly under the new administrations and the British didn't have the manpower to Police the whole country, or the finances, following WWII, to employ others to help.
The same thing happened with Rhodesia (now Zimbabwe). It used to be the "Bread Basket of Africa" under European rule but as soon as the European rulers were deposed it descended into chaos. Today it has to import most of its food and lives on Foreign Aid.
We live in unsettling times - see Trump, Kim-Jong-Un, Rodrigo Duterte and China's treatment of Hong Kong - and to a lesser extent the Immigrant/Migrant issue in Europe and the arguments over 'Brexit'. The Invasion of Iraq gave rise to "The Arab Spring", the removal of Gaddafi caused civil war in Libya, and so it goes on.
I think there will be more of this until something unexpected happens that causes people to take a fresh look at life and pull together. I'm afraid it will take something like a large meteor strike or series of major earthquakes/Tsunamis to achieve that, though.
Cue the Monty Python team with "Always look on the bright side of life" . .
Bob.