> The deaths that are most covered are a tiny fraction (<1%) of the way we die

They are precisely covered because they are exceptional. No one care about car accidents because that's a banal cause of death. But a plane crash is not. In countries like France where islamic terror attacks have became common place, small scale attacks causing a few deaths are not covered for days and days anymore.

Also event like a terror attack informs more about the state of a country and the world than an one suicide (suicide rate or aggregate can be valuable insight hough).