Can o worms opening coming up! You'll get a lot of differing opinions on this. Some areas you can't take things off the wrecks. Great Lakes for example. War graves. National historic sites. Others however are fair game. It's called salvage and if not for the people that do bring things up some might never see them. Saltwater wrecks have a finite lifespan. Displaying artifacts in dive shops, private collections, and the like may be the only reason these items do not just disappear into the muck.
As long as no laws are broken what's the harm? Your descendants not being able to see them? One good hurricane and they would not be able to see them either. Ok to see in a museum? What is the difference between a dive shop or someone's mantle and a museum? One thing might be that for every item on display in the museum there may be 100's that are packed away in a box that no one will ever see. Museums are notorious for locking stuff up that they have acquired and no one ever sees it except for a few people who expended no time, effort, money, or risk to acquire it.
I see nothing wrong with taking and preserving items by private individuals where it is allowed. The sea destroys and makes things disappear. Bringing them up stops that for that item.
I don't know how well you know the North Atlantic dive community (NY, NJ, Delaware, MD) but they were the pioneers in salvaging stuff from wrecks.