Anyway, to answer your question: because we already do a lot to stop the other causes. Cars have oodles of safety regulations, for instance. Home pools have rules on covers in many states, lifeguards are placed at water features. But we can't just snap our fingers and stop all car deaths, or cure all disease.
Meanwhile shooting deaths are an entirely artificial problem, which we actively do less than nothing to solve. Both by avoiding root cause fixes - not only avoiding addressing mental health, but actively encouraging bullying of minorities like trans students - but also avoiding regulation of the most effective tools (guns).
And, just a final point, humans are human. A kid dying in a tragic accident or disease is heartbreaking. But a dozen kids being eviscerated on Live TV repeatedly for someone's entire adult life, with tens of millions of people having the audacity to say "get over it, we refuse to talk about this" or "even "it's a hoax"? That's enraging.
We are emotional animals, but I'm more than happy that we try to leverage our empathy to make the world a better place. We can do more than one thing at a time, after all. For instance, under your argument, nobody should have bothered inventing amber alerts because it doesn't save hundreds of kids per year.