If there were a 100% effective (no false positive or negatives) gun to legal owner biometric ID thing, then that should reduce Chicago gang violence as well. The problem is I don't believe it's technically possible to build even a 90% effective system like that (a trigger and firing mechanism is mechanically simple; I could just open the gun and replace the advanced biometric system with a traditional one, perhaps 3d printed), and the are the 200 million existing weapons.
Biometrics are potentially good for preventing someone from taking your gun and shooting you with it (which mainly applies to police who open-carry in close proximity to felons), or potentially for keeping children from getting access (although a traditional safe or lockbox works fine for that).