You don't want things to break down in a landfill. They do decompose in industrial composting facilities, though, which are becoming more accessible (we just signed up for a service that costs $5/week for a decent-sized bin).

Wood doesn't break down under landfill conditions either, at least not on human time scales.

But wooden objects do biodegrade within human time scales if just left in a meadow. The same is true of polylactic acid objects. Neither wooden nor PLA objects break down in a home composting system like orange peels do, but both biodegrade much faster than e.g. polystyrene.