It's been stated in various threads that wooden construction tended to be heavier than aluminum construction. That, however, seemed to refer to aircraft that were designed to be metal originally, but modified to be partially or all wood due to fears of light alloy shortages. Granted, especially in terms of fuselage, the Mosquito, Hornet, and front of the Vampire and Venom fuselages were built of a sandwich material that was sort of an early form of composite construction that was very light and strong (so much so that Mosquito and Hornet fuselages, at least per cutaways, lacked a lot of the formers and stringers that most metal construction had.
So maybe weight was a consideration for not just the Vampire, but also maybe the Hornet. But one issue could be internal volumes for the Comet, which was a jet powered long range airliner. That thing needed as much fuel as could be safely packed into it, given that jet engines were fuel hungry compared to piston engines, and still keep it's load carrying capacity. Not to mention as a peace time airliner, it was hoped to have long service (issues with pressurization that were unknown at the time in the industry not withstanding).
But then, there was also production, too. From that standpoint back then, wood was probably cheaper and easier to work with, depending on the company. A Spitfire or even the Hurricane to a large degree needed factories that were tooled up for and a work force who knew how to work with light metal. For the Mosquito, de Havilland could contract furniture makers and wood workers to make components as subcontractors very easily. And a lot (not quite all, but most) repairs done to a Mosquito were easily handled by wood workers.
It's like what the late Ian Hogg said about submachine guns during World War II. Often times, high powered rifles, be it bolt action or let alone semi-autos, needed factories and workers tooled up for and skilled in working with stuff like metallurgy and metal treatments and such for high power, high pressure rifle rounds. SMGs, which were simpler to build and used much less powerful pistol ammo, could be made by small machine shops and metal working concerns.
In a total war like World War II, everything and everyone was looked at for contributions, and, especially among the British in 1940 when their back was against the wall, there was no shortage of volunteers who wanted to contribute something. And if nothing else--and even that can be seen as big--the Mosquito and other wooden aircraft of aircraft components did free up workers and materials for things like the Spitfire and other programs. And having Mosquito bombers, PR planes and night fighters and strike aircraft--on top of how well they did their jobs--was a hell of a lot better than no planes at all.
Not to mention this factor, that some things do allow other future items to be possible. In it's own way, the Mosquito did make the Vampire, Venom, Hornet, Comet and Sea Vixen possible, one way or another.