Ask any honest organization that monitors exotic wood consumption, and they'll tell you that >95 percent of exotic hardwoods are harvested for firewood or cleared for farming. Very little is put into the lumber market.
On a parallel note, consider the elephant population in Africa. In areas where hunting is allowed, there are plenty, if not too many, elephants. Does hunting increase elephant numbers?
Nope, the lesson is, governments will protect commodities of value. We have large elk herds in America because we value them, and as a consequence, they are protected. The huge amoount of money raised from license revenues funds conservation efforts to preserve habitat, etc.
Make exotic hardwoods value-less by not buying them, and the indiginous peoples where the trees grow will clear them to plant crops or what have you to make money. Not that exploitation doesn't exist in this day and age, but when dealing with subsistence living people, the forest has to pay its own way to be sustained.
IMH ranting and raving