My first thought is that any wreck should be left alone. This especially applies to historical wrecks, significant wrecks, war graves, or the ever popular "protected wreck.
This doesn't matter if it is in fresh or salt water. If the wreck is in danger of being ruined, then I believe that the wreck should be surveyed for historical/archeogical significance. If it is, the artifacts should be removed by trained divers working under the direction of a real marine "Indiana Jones"
If it isn't significant, and going to be destroyed (or has been professionally strippped) then maybe a mantlepiece is better than disappearing forever. Now of course - time to destruction is still an issue.
(Of course, when I discover a 1920's bootlegger full of scotch and whiskey or a Spanish Galleon full of gold things that got really lost in Lake Ontario.......... IT'S MINE! MINE I TELL YOU! ALL MINE!)
But a side question.... If you dove onto the Doria; would you take a plate?