Me thinks the answer certainly lies not in a "UNESCO" designation.  As soon as you tell people the place could no longer exist in the future, visitation increases and can make the disappearance more rapid.  Machu Picchu comes to mind, I think NPR just did a story on it, bless them, NPR.

Venice is a prime example of how excessive tourism can hollow out a community.  Mona Lisa is a prime example of the Everest effect, and its funny and sad to see pictures of the immense crowd standing around it taking selfies.  Quiet contemplation of the artist and his work? Nonsense! Selfie opportunity!