Would it be feasible to build a jet fighter plane based on a wooden construction? I read about the de Havilland Mosquito recently and that it was a quite successful British bomber in WW2 due its lightweight wooden construction. As far as I understand it, usual planes at that time were built mainly with metal parts already, thus heavier than the Mosquito and hence uncatchable for them. Furthermore it was too fast for getting hit by heavy anti air, namely the German 88mm cannon. 

With this traits of a wooden construction, I wonder if it is feasible to build jets mainly of wood and give them a boost in speed. I have doubts however that the wooden construction is stable enough for resisting the hefty g-force mid-air while flying in mach 3 speed.
The wings and a few parts of the body of the Heinkel He 162 jet fighter were made of plywood.
https://de.wikipedia.org/wiki/Heinkel_He_162#Konstruktion_und_Ausr.C3.BCstung

The Bachem Ba 349 'Natter', a rocket-powered interceptor, was built almost entirely of wood.  https://en.wikipedia.org/wiki/Bachem_Ba_349