From what I've read, biomass left on the surface decays quickly and contributes relatively little to soil tilth.  Matter left inches to feet below the surface and undisturbed by tilling tends to remain.  That matter consists of plant roots, not stalks and stems.

This points toward using zero-till, leaving an optimum amount of organic matter on the surface and returning all nutrients either as liquid effluent or ash.  If some of the carbon can be returned as charcoal (inorganic) and tilled in every ten years or so, the nutrient-holding capacity of the soil could be substantially increased at the same time as carbon is sequestered for millennia.

EP,

You are absolutely right!
(I don't often find myself agrreeing with you so wholeheartedly ;-)
No-till, leave as much as possible in place or return everything you don't use.
These principles are the essence of the Masanobu Fukuoka philosophy of natural farming. I believe such principles can be applied in varying situations with positive long-term results.
i.e. lower external inputs (energy, materials) and healthy soil.
Mr. Fukuoka has been analysing energy inputs versus energy outputs of farming since the 1930s.
Blinded by the "Green Revolution", most people dismissed his valid concerns about the disaster being created by "modern" farming methods.