prohibiting the possession, sale and trade of fins is the only measure that is realistically enforceable.
Having a clear ruling makes it infinitely easier for enforcement agencies, which are underfunded and understaffed in just about every single state. They do not have the capacity to police every ship at sea and they cannot control what is landed every day in every harbor. With shark and shark fins, there is the added problem of identifying species. In the case of fins, once they are cut off, they are often indistinguishable unless a DNA test is done, making it extremely hard to tell whether they came from endangered species or not. It is also hard to trace whether they came from state or federal waters, whether they were imported, transshipped at sea or taken locally. There are so many ways to get around the rules that enforcement becomes impossible.
A law that stops the sale and trade takes care of the majority of these loopholes, because it doesn't matter where the fin came from, why it was taken, or what species it came from. It can also be enforced on land (ports, airports, restaurants, shops, transport companies) and alleviates the problem of relying on fisheries enforcement, which usually takes place only at sea or at the docks.