I get that it "seems" that "gun violence" should be a public health matter for government funded health organizations to study. Would you agree that engagement in criminal behavior, and mental health issues that lead to violence are public health matters? "Gun violence" is such an overly broad term that drawing specific conclusions really isn't possible when only "correlated" with gun ownership. Gun violence occurs both in defensive postures, and aggressive postures, as well as accidental, and suicidal. All of those categories have to be broken out into appropriately constructed studies, rather than focusing on the "tool" as the "cause".
Stripping funding from the CDC for overly broad and poorly conceived/ constructed studies of gun violence IMO is a good thing. Nothing at all prevents OTHER privately funded groups or institutions from studying CRIME, or gun control, or gun violence. The problem with gun violence studies is that the CDC was straying into studying gun OWNERS, and drawing conclusions that were, at best, correlation, and then making LEAPS of statistically massaged logic into promoting those insufficiently supported correlations as CAUSATION. That is using propagandized and manipulated statistics to make political inferences under the guise of science.
No matter which political ideology currently holds power, or is occupying the White House, we cannot allow, encourage, or promote our publicly funded governmental organizations to conduct research to further a specific political ideology, as a means to incite rash policy changes. (Such as "guns are bad" or "gun owners are dangerous".) That strays dangerously into puppeteering qualities of banana republics, as well as arguably being pseudo science. (Like: "Some gun owners are under the sign of sagittarius, and guns are used in suicides and crimes, therefore sagitarrians cause suicides and gun crimes.")
Anyone can do a study on whatever they like. We put the brakes on governmental funding to private pharmaceutical companies that manipulated and massaged their scientific studies to ensure their drugs always performed positively in studies, and these same pharm companies actively avoided, or abandoned, or ignored, any data that was not encouraging for their products. That didnt mean no one could do studies on those drugs, but it did mean that we would not use tax dollars to support thinly veiled marketing studies on every new drug pharmaceutical companies developed.
Similarly, research on guns has devolved into research on gun owners as the source problem. The CDC doesnt study stabbings by attempting to quantify and correlate knife ownership as the cause. The CDC doesnt study DUI deaths by correlating car ownership as the cause.
It a chicken and egg argument. Those with anti gun ideologies believe the root cause of all gun deaths is the TOOL, the gun. Gun rights ideologies believe the gun is a tool, and that gun deaths have many CAUSES that should be addressed. Flawed studies start with a CONCLUSION (not just an observation), and work backwards to construct their study to illuminate what they have already determined.
A CDC study before the Dickey amendment speciously concluded that gun OWNERS were the problem. That study has been cited by politicians and commenters over and over and overwithout even slightly conceding that the study itself may not have any supporting evidence in the literature, may have been poorly designed, drew inappropriate causation conclusions, or may have had significant bias. That is a huge issue, because gun ownership is lawful, and is not simply a privilegebut a right protected within the constitution. Propagandized, weakly designed, weakly supported studies should not be funded by public dollars, or used to promote political change.
The public health issue that needs serious and longitudinal study is the antisocial actions of people who commit crimes, and the problems of those with mental health issues who commit crimes. That is where the CDC and NIH should be concentrating their research efforts. Root causes, and not tools.
Private groups, or private individuals, with an activist agenda, like the SPLC or the NRA, are free to conduct any research they want.
There are dozens/ hundreds of commentaries on the Dickey amendment, both for and against. Here is one that is sort of balanced:
https://www.theatlantic.com/health/archive/2018/02/gun-violence-public-health/553430/