Any study performed correctly will produce some results by eliminating or highlighting areas to work on, what gain is there in not allowing a study just because gun violence is used to focus it.
That wouldn't be the reason. How many "government studies" do we actually need anyway? If you've heard of the "Golden Fleece Award," you might see things differently. I recall that there was once a study to find out why prisoners want to escape from prison. Need I say more?
Mental illness is a large grouping and any results just studying mental illness will fail. Focusing on a specific illness or a specific violence allows for better results. Any logical person understands this.
Sure, any "logical person" with too much blind faith in the system would agree with that, but those of us who see things as they actually are would not agree.