This is where the solution to this should lie - personally, I'd like to see the Acropolis Museum and the British Museum (and all major global museums) unite into a global museum with branches everywhere. Access would be free at each site, knowledge and techniques freely shared between staff and exhibits which are of regional or global importance viewed in a proper context rather than narrow modern nationalist interest.
The Elgin Marbles could therefore stay in the same museum, but in its Athens branch. The whole history of the Parthenon could be shown, rather than a sanitized version of what 19th and 20th century people felt was important.