They don't burn the cane always these days do they? In fact, they have machinery which basically 'chips' the useless leaves which forms a trash blanket which in turn regenerates the soil (to a degree) for the next crop.
I could be wrong, but I believe there's less than 5% of cane crops being burned in Australia these days.
Aside from that point, you're right about everything else you've said about sugar cane dave.
(and I bow to your superior knowledge)