If we are going to globalize and begin expanding throughout the world, we cannot expect to preserve every relic of past human existence. I believe ruins of completely ruined cities that serve no practical purpose, shouldn't be preserved. Perhaps the land can be used for agriculture or homes for those who don't have them. Don't take this the wrong way though, I don't want to destroy the Great Pyramids or something of that sort, I just mean not every ancient relic needs special protection.
All past civilizations have an effect on their successors: Rome and Greece changed the political world, Europe as a whole changed the exploration world, etc etc. This can all be seen in the buildings, monuments, palaces, and cities that they built. The history of all nations was built upon these cities. By demolishing them, you destroy part of your culture and part of your history. One good metaphor would be this: if given the option, would you erase your first 18 years of life experience to make room for new memories, even if you still remembered what you learned in school? No? That's because if you demolish a monument such as Stonehenge or the pyramid of Giza, you reduce it to merely a document and a set of pictures, which cannot be enjoyed nor understood as well as the original.
No because think of this, Does a family want a document or precious heirloom to be destroyed? No they want to treasure it. So let them treasure it don't rob them of the only thing they have left, please don't take that treasure away from the world. Please its all we have left.