"Like water on a leaky roof"

That's how James Cuno describes the 1970 UNESCO Convention in a Q&A with Science News.  He makes some correct criticisms I think, but I differ with him on the ultimate remedy for these difficulties.  I think we need to start with an open antiquities trade in which the history of objects is published, open to the public, and even enlists 3rd parties evaluate the propriety of acquisitions.

What was the effect of the UNESCO 1970 treaty on looting of archaeological sites?

It hasn’t stopped looting. In fact, from what we hear, looting is increasing.  Looting is not a leisure pastime. People don’t decide to become a looter rather than being a lawyer. They are desperate people doing desperate things. In situations of a failed economy, a failed government, the absence of civil society, internecine warfare, sectarian violence, drought — whatever — conditions emerge that can create pressures for looting. Simply criminalizing the illegal acquisition of goods won’t stop looting. It hasn’t stopped the trade in drugs or trade in stolen materials of any kind.

So an important artifact with dubious provenance for sale on the open market, available for anyone else to buy, isn’t available to foreign researchers?

Right. So fewer and fewer things are entering into the public domain.  These export constraints are creating black markets. And like water on a leaky roof, looted artifacts are finding the path of least resistance to a buyer somewhere. I’ve heard they’re going to the Arab Emirates and Asia. What I can tell you is that they’re not coming to museums in the United States and Europe [which adhere to UNESCO 1970].

Just because other nations and buyers may be buying looted objects does not I think justify their purchase by North American institutions.  There are flaws with the Convention, but it has produced some important changes in heritage law and policy.  It has helped elevate the importance of national ownership declarations, and it has raised the general profile of heritage policy.  It has not yet produced a perfect regulatory framework, and though the convention has some drawbacks, we could also point to lackluster implementation or enforcement by many nations at the market end.