She totally could have. But other means of suicide give family and bystanders a chance to intervene. Pills and alcohol can be pumped out of the stomach. You can be pulled down from the edge of a bridge. You can rescue yourself from a hanging if you find you have last minute regrets.
A gun is brutally efficient at killing you; Load and pull the trigger. If the gun is lying around loaded, all you have to do is pick it up and pull. A gentle flick of the finger and it's over.