Actually, wood is a fine composite material. The 787 is largely composite. Why not the car? I like it. Also, check out the GP-4 aircraft. Or, Mr. ME-262, the English Mosquito :0)
As an aircraft engineer/inspector/mechanic/pilot/instructor/manufacturer I can tell you a few things about Aerospace composite manufacturing since it is something the company I run does. Wood is not a very good composite material. It does not like temperature or moisture variations either dimensionally or mechanically. It is soft and organically digestible. Its best application is the end grain balsa core in a hermetically sealed sandwich panel. Beyond that it is easily outperformed by other materials with better strength to weight ratios, better long term durability, better dimensional stability, better operating temperature range. Better chemical resistance, and on and on.
Give me the number of the 787 print that calls out Maple, Plywood, or MDF, for a structural part and I'll wire you a fat load of cash! I like the GP-4 but it is neither certified nor has it ever been in production commercially. It is labor intensive to build and could be made more efficient with a more modern type of construction. The kit says it comes with "all the metal parts prefabbed." Needless to say it is a good example of why most kit builders select a different type of construction.