DC’s argument has mostly come down to a pragmatic one, not a legal one. They claim that it reduces gun crime to reduce the number of guns in the city. If they really believed this they would not arm their police officers.
Since they do arm their police officers, they are acknowledging that it matters who has a gun. Since CCW holders are less likely to commit a crime with a handgun, than a police officer, it is obvious that this is about government power, and not public safety.
DC’s argument is absurd. Its logical conclusion is that “executions will continue until moral improves.”