If making it illegal to shoot people doesn't work, why would making it illegal to own a gun work?
Because people do stupid things in the heat of the moment. We know that, for example, putting painkillers in blister packs prevents suicide. Because it's easier to neck a bottle of 50 pills without thinking than pop 50 pills out of a pack then neck them. A lot of work on suicide is done to try to delay it, because if you delay it, it often doesn't happen.
Same with violence. If I am a man who is jealous about my wife's new relationship after a split, and I wish her and her BF ill, if I can just pick up a gun and go round, I might. If I have to consider how to subdue and hurt two people without a gun, I'm going to think twice.
Making things more difficult to do DOES prevent them. People will do things that are EAST (easy, attractive, social and timely). Make guns less available, less cool, less acceptable and you will have less gun crime.
Unfortunately violence in the US is also easy, attractive, social and timely. Military police forces, media all about violence, starting wars all over the shop. It's about as far from a cohesive, homogenous, socially equal and happy society as it's possible to be. And that needs to be changed too.