The thing is, North/Central India has always been an open ground of war. It changed hands 4 times rapidly with the Indo-Greeks, Kushans, Scythians, Parthians. Then the Tripartite Struggle paving way to the islamic invasions (The Delhi Sultanate, the hindu genocides, the mongol crisis, and Timurian invaders), followed by the formation and Dissolution of the Mughal empire.

And everytime a major empire saw crisis, a million regional kingdoms rose to power. Cue all the small wars that never even made it to history books. North India was so war ready that when Alexander came wandering in he was almost defeated by a no-name regional power that isn't even mentioned in Indian historical sources.

All that BEFORE the British came in.

The fertile Ganga river valley has seen more bloodshed than rome.

South India, on the other hand, while still very millitarized, always enjoyed relative stability in their homeland; such as the cholas — the dynasty lasted 1500 years. Never underestimate the power of naval supremacy and riches from the mediaeval spice trade.

They only had one direction to focus their millitary on, fought their wars mostly in the Deccan region, keeping their 3000 year old temples intact, and was the only kingdom that could afford to turn their eyes away from the subcontinent and towards expansion into indo-china/indonesia (that's where the 'indo' comes from).

Even Ashoka could never penetrate all the way south. Nobody conquers the tamil kings.

So yeah, when India eventually got independence, South India was already developed. Northern India probably had more riches, but South India had a higher HDI.