I don't know, but the stuff's legally theirs, and originating countries now want to welch on deals they made, usually to their profit at the time. You have to convince a museum that gets prestige and makes money off the exhibition of this stuff to give it up.
Most of the archaelogists of the early 20th century and late 19th were not shinning examples of scientific discretion when it came to preserving these artifacts.
I'm only talking about when they had legal permission.
"The Egyptians, Greeks and Peruvians are capable of acting as curator as well as we are."
"Capable", conceivable but not demonstrated.
And what of the sheer national instabilities in those places? At any time, in any Islamic nation, some whacko may destroy any statue or any artifact with an image on it.
Peru has always been a land of theft where the strongest took what they wanted. Far more artifacts have been "looted" by locals needing a bit of money, and far more sites ruined by said locals, than by archeologists from the First World.
Might I ask why you seem to insist that backward places are equally safe repositories as major Western facilities?