There is an enormous gap in understanding between the public and cultural resource professionals. Cultural resource professionals are those archaeologists, historians, and architectural historians who are hired to examine and protect the cultural heritage of a particular country.
In the United States, and many of the developed countries, Federal law (and a lot of state and provincial laws), require that proposed projects such as highways and dams which involve federal moneys must first have completed a cultural resource survey--both archaeology and architectural survey--to see if there are any buildings or archaeological sites that might be damaged by the project. The cultural resource professionals identify the historic properties which exist in the vicinity of the project, and make recommendations. If a property is determined worth saving, that site is recommended for protection or "mitigation" of the negative affects of the construction. The official final decision is not made by the archaeologist or architectural historian, mind you; but the professional has an enormous amount of input into that decision. The problem is, what cultural resource professionals consider "worth saving" is not necessarily equivalent to what the public sees as "worth saving." I think this problem can be summed up as "sacred sites."
Sacred sites, in my admittedly peculiar usage, are locations that people--all people, a segment of people, a handful of people, or even one person--hold dear to their hearts. Everyone has sacred sites, places where special events happened or that have personal or cultural significance or are just plain pretty. We all would like to see our personal sacred sites preserved if possible. We'd prefer them not to be destroyed by the urban sprawl of cities, or looted by people who want to take the beauty home with them and forget the rest of us, or even encroached upon by cell towers or telephone wires. On this we're all agreed; even people who loot archaeological sites or build development projects have their own special places; they're just not the same as ours. The preservation laws which exist in many developed countries were created to protect these resources.
But the real gulf in understanding exists in the definition of what is "worth saving" as used by preservation professionals and misunderstood by members of the public.
What the public doesn't often understand is that the decision to save a site almost always boils down to integrity; in other words, the value or "sacredness" of a site is established not on its importance to people or a particular set of people, but whether the site contains enough intact information to justify its protection. This is a fundamental gap, because to most normal people (once upon a time I was one, so I can say this), "physical integrity" has nothing to do with "sacredness."
The problem is, "sacredness" is not measurable; and successful federal laws can only be made over the measurable. Successful science, in fact, must rely on the measurable. But--is this what preservation laws were meant to do? Until we can bridge the gap between "sacred" and "valuable", either by clear explanation of what we are preserving and why, or by some magic process figure out how to measure the unmeasurable, this gap will continue to exist.

