Buried Treasures Should Stay Buried

Most of the time:

[James Delgado, director of the Maritime Heritage Program at the National Oceanic and Atmospheric Administration (NOAA)], who has excavated wrecks for archaeology institutions throughout his career, says the litany of unknowns is part of the explanation for why wreck hunting is so expensive. "The street value of shipwrecks is minimal. Generally it's a losing proposition, except in a few cases, because it costs more to find them, work them, and deal with what you find. An average mission in deep water can run into the millions, and that's just to find it. For every dollar you spend looking and finding, you'll spend about $10 excavating and treating what you've found [to offset] chemical changes that happen underwater." 

And then there's the question of whether you can keep what you find. Governments, insurance companies, and anyone with a chance at a legal claim will set their sights on recovered treasure.