Er, as someone else has stated...
There are specific salvage rules already on the books for this. They ARE NOT AT ALL what you would expect, I can almost guarantee that by the tone you're taking here.
There are also good reasons they exist as they are. Yes, it does hurt the original owners sometimes, but overall they are a great tool.
Lets say you have a nice 60 foot yacht.. You're an idiot, and somehow run it aground on some sand bar somewhere, thus posing a navigational hazard for other vessels. If you abandon your ship, I can come right in tow it away, and keep it pending an admirality(sp?) court ruling on what a "reasonable" salvage fee is, etc. From my understanding, in many of these cases the actual vessel is simply written off by the insurance company and the salvor usually simply keeps it.
The same also applies to cargo. The laws are on the books to promote salvage of materials/vessels that would otherwise pose navigational hazards and/or simply be abandonded.
So yeah, you could like simply take your abandoned container full of BMW motorcycles, report them as salvaged to whatever governing body it is that has jurisdiction, and very well likely they would simply become yours. Salvage laws are "working" in this respect - a huge amount of crap on the beach is no longer waiting a few weeks/months for an insurer to get off their asses and pay for the cleanup.
Of course, you're getting into one of the most complex and specialized law areas of all time, so what I said could be absolutely false

However, I think the underlying idea is conveyed.
So yeah, in modern times the laws can certainly be used to "screw" original property owners. However, those risks are extremely well known by any company that operates vessels on the high seas, and it's simple economics at work in most cases. I bet it's cheaper for them to simply write off that cargo and not worry about all the details.
But to answer your question.. No, I wouldn't feel quite right taking that property off the beach. Even knowing that in all likelyhood it will NEVER be returned to the original owners and simply thrown in a dump somewhere. I'm torn on it for that reason - it simply seems wasteful to not "rescue" the items.
For a fun and interesting time, try to find a lawyer who is familiar and deals with admirality/salvage law. They always have some real interesting stories to tell. One of the few areas of international relations that are intriguing to me.
-Phil