it is the fact that the nozzle is embedded in the fuel. Much more fuel than available oxygen. So, the oxygen is consumed near the nozzle and after a short distance, there is no oxygen left to spread the fire further away.
So you are right, 100% of the intake air is used. First the char is burnt with the oxygen to CO2 (and heat released) and after that reduced with more char to CO (and heat consumed).
How far this is spread out is dependent on the fuel size: Big chunks have little surface compared to the volume, so the reaction zone need to be larger. Small pieces are vice versa, but the flow resistance increases if they are too small.
So for your imagination of the interior of a simple fire gasifier: It is a glowing ball of coals starting at the nozzle surrounded by more coals. As they are consumed, the surrounding coals drop in the glowing zone.
Hope that is a bit helpful for you.