The reason we don’t use air core transformers for high-power, low frequency transformers (such as those used in power distribution systems) is because air core transformers have much lower inductance than a comparable transformer wound on a core with significantly more permeability than air. read more
If we use wooden piece in place of magnetic materials then Transformer will not work at all because wooden core can not provide path to the flux so flux will not link either in secondary side or primary side. In short Transformer will not work. That is why we don’t use wooden core in a transformer. read more
Wood is a insulator but have low reluctance than air so if you are using a wooden core in place of iron or steel core in the transformer than leakage flux is very high so losses are very high and mutual flux is very less so the efficiency of the transformer is very less. read more