Divided by DNA: The uneasy relationship between archaeology and ancient genomics
nature.com
nature.com
To me, objections to genetic methods in Archaeology and Anthropology are a sign that they are more interested in presenting a specific interpretation of history rather than discovering the truth.
What this ultimately means is that genetics alone are not sufficient to precisely capture what we're interested in, nor are traditional archaeological/anthropological methods. You need to reconcile some very different types of data into a synthetic whole. The general problem of how to do this is still being explored.
America is a perfect example of the latter, where Native Americans and their culture were largely replaced by Europeans both culturally and genetically. Of course Native Americans and their cultures still exist, but they are no longer dominant in North America. A genetic analysis would confirm that Native Americans didn't simply start building European style cities in the 1500s, they were essentially displaced by another people.
This is the question that I find the most fascinating, and I am glad to see that I am not alone. If a new people did arrive, did they adopt some of the cultural practices of the people they displaced? Did/do humans tend to recognize places of spiritual importance and continue to honor them out of respect for/fear of the ancient gods of a place that they are new to? Displacement with or without competition is a major feature of biological evolution, it would be surprising if it _didn't_ apply to humans.
I think a good example of some part of this is southeast Asia. Cambodia, Burma, and Lao are all adjacent to Thailand. The people that makeup these 4 nations visibly share an extremely recent common ancestor. Yet, the cultures and groups of peoples are all quite different and there is even extreme 'racism' among them, which is somewhat ironic.
If you studied these people based on genetic makeup from a distant future it'd just look like a mostly homogenous glob, but that's not even remotely close to accurate. And so an interpretation based primarily on genetics would be completely misleading.