Agreed. The museums should have first refusal for these artifacts but must pay fair market value. If they will not pay fair market value they are simply thieves. There have been hundreds of old Spanish wrecks salvaged by private enterprise. How many have been salvaged by governments? These salvagers are doing a service to history. They are bringing back the past for us to admire and see. If a government or museum is not willing to pay the fair market value these goods should be sold as the governments and museums have by their inaction determined them to be not of importance.
But who will they pay?
For instance, the Black Hills Institute paid 50K for the rights to dig dinosaur fossils and found "Sue", the most complete T Rex known. While in the midst of preserving the fossil, the Feds raided them, saying it was on Indian Land and it was a Federal matter. The dinosaur fossil was confiscated, then sold to the Field Museum in Chicago for (IIRC) 8 Million dollars.
How much did the Black Hills Institute (professional but non university affiliated scientists) who found, excavated, and were conserving the fossil at the time of confiscation get paid?
Bupkis.
If people are going to go look for treasure, they will want a better return than socialist minimum wages. Years of effort and expense are involved, and will go uncompensated if nothing is recovered. There has to be an upside to that risk.
The other result of this crap is that kids no longer dream of finding treasure or even arrowheads (cultural treasures), because they don't have a chinaman's chance in hell of keeping the stuff they find (or being able to sell it) if they do.
That means the future archaeologists, historical researchers, geologists, and paleontologists will simply not be there.
That sense of adventure is one of the things that has inspired Americans for centuries, the dream of finding their fortune over the next hill or under the water.