I'm watching Raised By Wolves, and I'll try to keep any spoilers out but you might scroll past anyway.

Burning organic matter means half of the nutrients in the material float away with the wind, so you don't want to combust it for any reason (and especially not for disposal, which is currently my biggest beef with the show).

So I like biomass, and I don't like biomass. As I understand it, you can limit your losses in that respect by separating your ramial (young) wood out. It's higher protein and nutrient content, suitable for composting if done correctly. But most of your coppice is going to be ramial wood, so where's your sustainable harvesting angle?

The only tech I know that completely avoids that problem (Super Critical Water Oxidation) requires pressure vessels and very high tech ceramics. Last I checked it was so expensive they only used it for superfund site cleanup. Turns out salts become highly corrosive at high pressures and temperatures, and there's a triangle of heat, pressure and corrosion for ceramics, so you need ceramic composites to build a reaction chamber with any sort of durability.

You wouldn't want one of these in your basement, let alone your kitchen.