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Is there a tradition?Obviously yes, otherwise it wouldn't be contentious.
There are many reasons to salvage shipwrecks, some better than others. Wrecks which pose navigational hazards are obviously removed. Wrecks which contain hazardous materials (oil, nuclear waste, explosives, etc) may also be salvaged. Wrecks which contain valuable materials are also sometimes salvaged, and in rare cases ships may be raised and refurbished to be used again (this happened to the confederate submarine Hunley twice.) There is no hard and fast tradition on salvaging ships, it exists on a continuum of necessity to reviled grave robbery.
Specific instances can be evaluated on that continuum. The K-141 Kursk was dismantled and partially raised, in large large part because it contained a nuclear reactor and several nuclear warheads; I think most would agree doing so was prudent. On the other end of that spectrum, numerous ships sank during the Battle of the Java Sea have been destroyed for scrap metal, which has been widely reviled as grave robbery. (The steel of those wrecks has some value because it dates prior to the nuclear era: https://en.wikipedia.org/wiki/Low-background_steel) but "it's valuable tho.." isn't generally seen as an acceptable reason to molest these graves.
I think retrieving artifacts from the Titanic to put on display falls closer to the "grave robbery" end of this spectrum.