First of all, what defines "sustainable management"?
Who defines it?
Many populations of the animals we seek to protect are dwindling as a result of climate change, habitat loss and human conflict. Do we set management sustainability according to these downward trends, or do we seek to mitigate those trends with more conservative management? Do we leave it up to an agency that has the word "trade" in its name? When did we cede all ethical decision making to economic and trade organizations?
The rebound of the vicuna is a weak example. For years, the animal was poached for its coat. Then, people found that one could shear the hair of the animal to produce a fine wool yarn. Wish that worked for every commercially exploited species.
You cannot garner pelts, skins, claws, et cetera without killing the host animal. Sure, you can extract bile from a bear's gall bladder without killing the animal, but the bear inevitably lives its life in horrific conditions as a harvested creature. Some believe that we could harvest elephant tusks and rhino horns from living creatures, but the viability and ethics of that are quite suspect.