I am an agricultural scientist in the UK.

Burning stubble is a very useful method of weed control, especially for grass weeds. Weed seeds are shed into the stubble and most are destroyed when it is burned. There isn't any alternative method of seed destruction at this stage of the crop. Ploughing can help destroy seeds if they are ploughed down and left for long enough but of course ploughing releases CO2, one of the (fairly spurious) reasons for the stubble burning ban.