Stubble burning sounds like one of the dumbest ideas ever. Just leave it there and plant through it with your no till drill.
Leaving the residue on the field means your soil is protected against erosion and from exposure to the sun. The carbon in the residue isn't relevant but after three years the residue has decayed enough for the trapped nitrogen and phosphorus in the plant to become available to the soil.
In the North (Haryana, Punjab, western UP) you have 3-4 harvesting seasons with maybe a week between each other. Leaving stubble means you lose out on a harvesting season. If you want to maximize subsidies and your profit, it makes sense to quickly burn stubble and start afresh.
Leaving the residue on the field means your soil is protected against erosion and from exposure to the sun. The carbon in the residue isn't relevant but after three years the residue has decayed enough for the trapped nitrogen and phosphorus in the plant to become available to the soil.