Admiralty Law, nor the Law of Finds, were never set up with shipwrecks in mind, but for other ships to render aid to vessels in distress, without liability, and with a mechanism for reward for that aid.
The Law of Finds was simply for items found on beaches or floating, for a entity finding the cargo, to have a mechanism for a reward for the recovery. Before this, the owners would typically just go and take the items back. Currently, the Law of Finds requires for a finder to bring the recovery physically into the Courts possession, turn the recovery over to the Court for disposition, and the Court administrates the claims against the recovery. It is relevant to understand that the Law of Finds specifically is set up to administrate a fee to the salvor for the recovery, not the recovery itself, so technically, the recovery is actually the property of the Court. The owner has the option to pay the fee with the recovery, but this is not automatic. Historically, the Admiralty Court auctioned off the recovery, and the finder was paid from the proceeds of the auction, and that mechanism is still in place.
The laws of sovereignty apply worldwide, with many laws such as
UNCLOS governing the International waters and charter States. I cannot see how any member State, including the Bahamas, which is still part of the Commonwealth, ignore sovereignty and comity.
What is very interesting is under the Admiralty Law, and Law of Finds, only what is physically in the Courts jurisdiction, or brought into the Courts possession, can be administrated by that Court. Hence an Admiralty Arrest in International waters has little or no value, and currently, little means or avenue of enforcement.