Anthropology

In us so that Neanderthal did not entirely disappear.

I also would echo your question that, if Neanderthal was so inferior, why does its DNA survive in us?

Regarding benefits of DNA to the individual and how it might be adapted to other areas of medicine, I'd like to see a study of some DNA comparisons, if the proposed people would be willing to go along with it, of DNA from sub Saharan Africans who lack Neadnderthal DNA with people who have Neanderthal DNA. Genetic samples from around the world, with disease histories of each region might help to determine the benefits and vulnerabilities of DNA variations. Both Neanderthal and Denisovan DNA are higher in Asia than in Europe. Denisovans DNA is highest in Southeast Asia. It is absent in some other regions of the world.

Maybe comparisons of specific diseases and their presence, recovery times, and severity in different populations with and without Neanderthal DNA from specific DNA segments might give insights into possible uses of gene therapy for treatments. Is there a notable difference between people with no Neanderthal DNA and those who have it in varying degrees? Are there segments of Neanderthal DNA that are more harmful to us today than helpful?