In 1972, the surgeon general made a report that established the link. I see it as a cultural and social issue, concerning how people relate to media narratives. Medical authorities can contribute to such a discussion, but it would be a mistake to assume that their expertise extends very deeply into social and cultural matters. Medical intervention in culture has been a disaster, going back to the doctors who shut down the playhouses in Elizabethan England, and to the doctors at the turn of the century who insisted that women had no place in higher education because they were physically incapable of withstanding the pressure. The thousands of studies that you cite come from a fairly narrowly defined tradition called media effects.
Researchers show kids distilled, violent images that are devoid of any narrative context.
Often, the images have to be constructed by the lab because researchers can't find media violence without any narrative context. Researchers expose kids to these images in a laboratory and assume this is equivalent to the social and cultural space where media are actually consumed. In fact, the context in which something is viewed matters tremendously in defining what it means and how it affects an audience. It's very good at measuring sweaty palms, an adrenalin rush, and so forth, but its practitioners are not very interested in understanding what those feelings mean for kids. They don't explore the connections between the results in a laboratory and actual behavior.