Alot of these 4-star collections in the real world....are basically stolen or simply taken. You could totally downgrade the top ten collections throughout the world if you forced them to admit real ownership. I can see the point where the original country ought to own the item...but if a hundred years has passed...it makes it difficult to say who owns what.
I've thought about this a bit and believe that if the artifacts were not taken out of the country in some clanedestine manner, then they belong to the finders.
Just because nowadays they look back with regret at the lost tourism opportunities, does not mean all the artifacts others funded the search for should be returned.
I would possibly make an exception for mummies. Those are people with possible descendants alive now, and I could understand not wanting my great great granddad on display in a museum, or even my collateral great great grand uncle. I'd expect compensation for the expedition costs, though.