Of course we’re allowed to collect data on gun violence. The government does it all the time. The CDC is the only outfit that isn’t allowed to conduct research on it because some people don’t like how they conduct and present their research.
I don’t have any problems with the CDC doing research or funding research but I understand why people were annoyed with the CDC “public health” approach to gun violence rather than the FBI “criminologist” approach to gun violence.
My understanding is that the public health approach focused on banning guns as an effective method of reducing gun deaths, but the prevented gun deaths were almost entirely suicides. They also presumed that these suicides would be replaced by the typical “attempted” but unsuccessful suicides rather than other equally lethal methods of suicide. The CDC also doesn’t place very much weight on the increase in crime victimizatiojn that might occur in a disarmed citizenry with armed criminals unless people will die as a result. So if the CDC starts looking at this from more of a criminologist’s perspective, I don’t see why anyone could reasonably object but the suspicion is that these people aren’t built to look at these problems in that way.