They were originally sold with certificates of authenticity from the firm handling the sales, which was directly affiliated with the people who made the recoveries. I have a piece of coal from Titanic, which is the first stuff RMS Titanic Inc. recovered from the wreck.
Call me weird, but the engineer in me would rather have a piece of the hull with iceberg damage. I would get a feeling of morbidity from personal possessions.
Decidedly not weird to me; I'd feel exactly the same. My piece of coal is just a raw chunk, not gaudied up by being placed into jewelry or something like they're currently selling (that turns me off). I wouldn't mind a recovered coin but a personal possession (legalities aside) wouldn't pass the Gut Test.
The FBI eventually returned most of the $20's from D B Cooper's ransom to the boy who found them. I know they got slabbed and sold, but missed the chance to buy one. To me those are more fun to contemplate owning. Although I admit the notes from the Titanic are something to see.