Maybe it's just me, but I think a certain percentage of these types of finds should be archived, documented as to their location, then left alone.
We don't know what another hundred years of science tech will bring us, and what we might find if we wait.
And I guess it seems sometimes we are a bit timecentric, who says we, in this generation, own all the mummies that can be found in the Valley of the Kings?
Later generations might view us as a little conceited.
A lot of people agree with that, and there has been some movement toward very tiny excavations on some ancient sites. Sometimes that's sort of an accidental result (Mellaart got kicked out of Turkey over something else, and couldn't continue his excavation of Catal Huyuk; although I may have the chronology of events loused up), but work at Pompeii has slowed to nothing, with most of it done in the area of conservation work on already-exposed parts of the site. Also, non-invasive techniques are used to maximize the value of a dig, or to examine mummies and tombs.
But people today study fossils that were dug up years ago because they were preserved in museums. If we put them back, who knows what could happen. Some kid could pick one up and it'll be gone forever.
On the other hand, how many artifacts and finds can be lost/destroyed in the course of a century? Wouldn't it be better to analyze what we can and do our best to preserve them for later for reanalysis if new methodologies are discovered?