I'm not sure where you're getting busywork from. The idea is that future generations of archaeologists will have better techniques, just as the current generation have better techniques than those in the past. That they will be better at gleaning information from sites. And because we don't know what exactly they'll need to do that, it's better to preserve sites as much as possible.
The trouble is that "learning all we can", particularly if that means pulling artifacts to display in museums or leaving a site exposed to the elements, is a destructive process. Context is lost, which means information is lost. Future archaeologists can't stand on shoulders that aren't there.
Most of this work is extremely non-glamorous. Archaeologists spend a lot of time digging through midden heaps. A friend did his fieldwork in Iceland, where he mostly looked at fish bones and the rotten wood of what was once a structure or a longship. None of that stuff is going to end up in a museum, or being a tourist attraction.
It seems overly pessimistic to assume that all archaeological sites are going to be destroyed in the near future. To the extent that they are threatened by climate change or war, this can be anticipated and dealt with accordingly.