I must agree as to the loss of our underwater history when a site is destroyed by treasure hunters. Given that, there is some justice on the side of the treasure hunters when they say that the wrecks would be ignored by academia.

Perhaps a compromise could be offered: when the treasure hunters find - by very expensive searching - a long lost wreck perhaps the archaeologist could do the recovery/excavation and after retaining a few representative samples of the treasure turn over the balance to the "treasure hunters". A single coin with explanatory placard is all that is needed in a modern interpretive display.

After all, the discoverers are entitled to the booty if it is in international waters.
Knowledge will not be harmed by not possessing the gold.