Almost any domestic wood is sustainably managed. Unless there are other reasons to take land out of production, like development, which does not fall under this discussion, its a rare landholder that does not expect to continue harvesting lumber on land that already yields product. While some are more "actively" managed than others, the general aim is to be able to continue harvests.
Its worthwhile to ask about exotic woods because sustainabilty practices usually benefit the smaller land holder and/or workers in 3rd world countries for the same reason it benefits those in the US. Land can yield product but also be used recreationally (think hunting lease) is but one example.
Joshua, who with his Dad managed 200 acres of woodland for saw and veneer logs, habitat, focusing on specialty markets, like woodworking - carvers, furniture makers, turners and probably bowyers too.