Wood has a great weight/strength ratio (like CRP ), it's cheap, easy to work with, saves metals for something else, you can use furniture factories. British and Russians did it in Mosquito and La-5/7 production. Why Germans didn't do the same ?
The Germans certainly tried to use wood!
Noting the success of the Mosquito aircraft, the Germans set out to make a similar plane, the TA 154 Moskito. Which is a bit on the nose to be honest. However the Allies managed to successfully bomb the factory that made the sort of glue of sufficient strength for aviation purposes (tego gluefilm).
This was the only factory making the stuff, and the replacement adhesives proved to be entirely not up to snuff (with post-tego prototype TA 154s suffering loss of wing structural integrity and the ensuing problems with airworthiness. At the same time, the TA 154 was competing against the HS 219 which had the advantage of not having to rebuild a specialist factory to get into production. With the glue problems remaining unsolved, the HS 219 went into production while the TA 154 was abandoned.