Egret, setting aside politics, which can never happen, making this mere speculation about where they’ll do the most good.  It’s hard to decide who could most easily do without them.  However, I think they would have their greatest positive effect in their places of origin. 

But how about the politics?  I suspect we each will answer according to how just we determine the cause of the diaspora: an unequal balance of power called Imperialism.

I know that here in the USA periodically we bemoan property ownership moving to foreign hands.  Likewise jobs, natural resources etc.

Early on, the entirety of what is now the North American continent was available virtually free of charge, as were the antiquities you mention.  The first into the game of capital acquisition found the whole concept of capital lacking in much of the world, and took advantage.

There are deists, who insist on the reasonableness of the hierarchical enthronement of the fittest at the game of capital acquisition, who may cry foul when the game changes, but it already has.  Countries of origin are gaining the political will and clout to get back their cultural treasures.