Burning wood is not carbon zero. It is the reverse of carbon sequestration in the sense that atmospheric CO2 was once converted to wood by the tree, and now the wood is being burned and the captured carbon release back into the atmosphere.
That could be nearly carbon zero (I don't know the contributions from soil and what mass remains as ashes, etc..), except when you consider the opportunity cost.
That burned tree, presumably healthy just prior, loses the ability to sequester any more carbon. A burned tree puts carbon in the atmosphere AND removes a carbon sequesterer simultaneously. That act is removing X amount of future sequestration until the tree would have naturally died and turned to soil. At that point most of that carbon would still be in solid form and not in the atmosphere.
I'm nitpicking at this point, but I lean toward burning wood as not carbon zero for the sake of opportunity cost.
It really only makes sense to measure the carbon capture at the level of the forest. When a tree is cut down or dies, it makes room for other trees to grow. Removing mature trees that are no longer growing very much can increase the rate of capture. Removing trees that are growing quickly and replacing them with smaller trees could reduce the rate of capture.
Either way, there is a limit to how much carbon a given forest will capture (rot releases it just as well as fire) and it will only do it for the life of the forest, which is usually not a geologic time scale.
Biochar is a potential solution, although the technology isn't there yet (at an industrial scale).
If wood is heated in an oxygen free environment it will turn into a form of charcoal. At the same time it will release gases (like methane) that can be captured and used as a fuel separately.
Rather than burning the charcoal, it is put back into the soil which effectively traps the CO2. This also improves the condition of the soil and reduces the need for fertilisers.
That could be nearly carbon zero (I don't know the contributions from soil and what mass remains as ashes, etc..), except when you consider the opportunity cost.
That burned tree, presumably healthy just prior, loses the ability to sequester any more carbon. A burned tree puts carbon in the atmosphere AND removes a carbon sequesterer simultaneously. That act is removing X amount of future sequestration until the tree would have naturally died and turned to soil. At that point most of that carbon would still be in solid form and not in the atmosphere.
I'm nitpicking at this point, but I lean toward burning wood as not carbon zero for the sake of opportunity cost.