A 2015 prototype, in which a wood stove used for cooking and space and water heating was equipped with 21 thermoelectric modules cooled by a pumped water system, showed a power production from 25W (burning 1 kg of pine wood per hour) over 70W (4 kg wood/hour) to 166W (9 kg wood/hour).
So, it takes burning 1kg of wood to generate 25 Wh, or 90kJ. One kilo of wood contains, roughly, 20.000kJ of energy. That's about 0.5%.
It's fine if you want heat at that time, but quite a bit power demand is when you don't need any heat.
It also creates huge problems with particulate pollution that are tied with all fossil fuel heating systems.