Burning wood only becomes unsustainable when it is done on a commercially viable scale.
(I live rural and have a wood burning insert and a fireplace. I don't use them much anymore.)
It was “sustainable” only due to small population.
It is green in the sense that logging a forest net sequesters carbon from the atmosphere. Yes, even if you burn the wood. There's still carbon left in the ash and from discarded branches, and forests are most productive when regrowing.
You are right they are not healthy. The air pollution generated is nasty and even with a good catalyst stove cannot be reduced very much.
That's right! Then everyone will have to buy this expensive heat pump sold by few corporations around the world! It is only green when it fills correct pockets.
Burying biochar (carbon and minerals left over after gasification of woody biomass) is one of the only means of reversing mining of carbon (coal and petrochemicals). The carbon that you introduce into the soil as biochar has a carbon lattice that is fairly inert and can remain in the soil for thousands of years. It also improves the soils friability, moisture retention and ability to harbor micro-organisms.
Lastly the plant matter that you're burning has absorbed it's carbon from the air, and is one of the only ways to "draw down" CO2 from the atmosphere. You're working within the carbon cycle, removing fuel that will either compost or result in wild fires and be released into the atmosphere anyways...instead of using petrochemicals to produce heat and power.
Many of these gasification systems run fine on dead standing wood (fallen branches), corn stover, biogasse and nut shells. So you aren't even utilizing woody biomass that would be used for lumber construction, just the agricultural waste products.