I believe that violent movies and video games do desensitize some/many people to violence, esp when there is no concomitant moral education. We used to have violent entertainment (usually cartoonish) alongside basic morality - contradictory but effective. Now we have snuff streams and zero morality.
Yes, for me it's more the lack of moral education than the depiction of violence itself. And the desensitization certainly has contributed to an opening for fascist ideology to take hold.
We used to have campy "violent" TV and Movies, the A-Team ridiculously blowing up jeeps and Rambo firing a machine gun from the hip. That's all transitioned to "realistic" SWAT raids and war violence. Desensitizes and leads to everybody thinking they are an expert on military/police tactics.