This assumes global cultural value matters more than the native cultural value of the people to whom the artifacts belong.

I think the default should be to return to the native country wherever possible. Although it does beg the question of what to do if the native countries have changed significantly due to imperialism/colonization, idk.

But I do appreciate the value of cross cultural sharing so perhaps museums could have a rotating selection that they can borrow for some time from the native country, as long as the transport does not have negative impacts on the artifacts.