Cuno gets featured prominently, perhaps because of his strong arguments that many objects should remain in museums in market nations. He also extends the argument of the late Paul Bator, who in his seminal "An Essay on the International Trade in Art" 34 Stanford Law Review 275 (1982), argued that many restrictions on antiquities, including strong export restrictions serve to increase the black market.
Bennett's piece is a good overview, and a good introduction to some of the core debates in the antiquities trade. By necessity he paints many of these restitution claims with too broad a brush though. He writes
Along with Italy, the governments of Greece, Guatemala, El Salvador, Peru, Turkey, China, and Cambodia, among others, have pushed to reclaim prized artifacts from collections around the world. They have tightened their laws governing the export of antiquities or intensified the enforcement of existing laws and international agreements; they have made impassioned public cases on the world stage.
I don't think these nations of origin have in fact increased their domestic legal schemes; in nearly every case he mentions here these nations have had very strong legal regimes for many decades, some dating to the very beginning of the 20th century. Italy for example has a national patrimony law dating to 1939. In some cases they are working more closely with the US State Department under the Cultural Property Implementation Act. However, the main difference is the prominent Italian claims of late, which were the result of one fantastically successful criminal investigation which implicated an Italian dealer named Giacomo Medici, and by association his buyers Robert Hecht, Marion True, the Getty, MFA Boston, and the Met.
This allowed for the return of these implicated objects; of course the claims for return were bolstered by photographic evidence of many of the Nostoi objects, which clearly indicated they were illegally excavated on a massive scale. This is a far different argument than the one for say the return of the Parthenon Marbles, or other objects acquired during colonial times, or for the return of other objects which may have been acquired legitimately. I think we need to be particularly careful not to lump too many of these restitution arguments together, and indeed to be honest about how and why objects are returned. The salient issues remain: how are nations of origin protecting sites domestically, how do market nations respond to illegal activity, how are museums acquiring new objects, and is the market conducting the needed provenance checks? That is the only way to prevent future illegal activity.