Kaleea, archaeologists do not turn up their noses at sites less than a few hundred years old. Here in Canada, very careful excavations have been carrier out on sites from the 19th century, and the same is true in other areas as well.
Hrothgar, archaeologists do use all tools from a whisk broom and dental tools to the most sophisticated spectrophotometric analyses, DNA, etc. etc. Their "digs" take careful account of stratigraphy, and removed materials are carefully screened. Many valuable sites are still being partially destroyed by potholers, metal detector wielders and the like.
Here in this province of Alberta, laws protect fossils and archaeological materials on private as well as public lands, with a schedule of penalties including very stiff fines. Important cultural artifacts are similarly protected. Many other jurisdictions have or are enacting similar laws. Of course the unscrupulous or ignorant still take a toll.