It doesn't address the root causes of violence in our society. In fact, it may do harm in the sense we'd be so busy slapping ourselves on the back for accomplishing some good, we'd merrily continue the work of avoiding root causes.
But if we got the handguns down to the amount floating around in the rest of the civilized world, it would be a lot harder to walk into a public place and unload a shitload of rounds before anyone had time to respond.
Shotguns and rifles can still kill people, but they don't serve that mass shooting purpose nearly as well. Semiautomatic rifles are more difficult to conceal. Shotguns won't shoot as many rounds so quickly, and they are less likely to kill as many people.
Same with gang gun violence, but again, that's a different problem, with a different set of causes.