Bill Tindall, E.Tn.
If you insist on including what we commonly refer to as the tropical hardwoods into the equation then US hardwood production (which is largely Appalachian, commonly defined as GA to PA) is not even half the world production. The leveling of the rain forests in South America and East Asia dominate.

If we limit the definition to temperate zone hardwoods (add birch to previous list) then the US dominates the production of "hardwood" lumber that winds up in furniture and architecture, excluding hardwood that winds up as paper and construction material. There simply isn't a lot of temperate zone land suitable for hardwood tree growth that has not been turned into agriculture land. Europe got clear cut in 987 AD and what was left in eastern Europe the Russians leveled after WWII to launch their "agriculture revolution.

Someone from our hardwood lumber industry that did mission work in Romania told me they had excellent hardwood forests but they were underutilized. We hiked all over Czech Republic and I didn't see but scrappy beech in the forests. But there were stupendous white oak and linden preserved in parks.