There's too much money to be made in the illicit trade.The price of a banned animal will rise and "some" people will not be able to bypass the high profits to be made with them.
On the other hand,if an animal's trade is banned and people stop or just slow the harvesting of them,then we could be looking at an overpopulated and weak group of critters that would be even more likely to spread disease.
In the U.S.,our furbearing animals are carrying more rabies and other diseases than they once did,because they're overpopulated.
The overpopulation is caused by being under harvested.The anti-fur campaign in America has caused prices for many animals to be so low that many are hardly worth catching.