A couple of summers ago, I taught a cycling skills class. For the last session, we went out riding. One of my students fell while she was behind me. I didn't see her fall, and no one can explain exactly how it happened, but the upshot was that one of her brake levers impaled her thigh and was entirely submerged. She had upright handlebars, and the brake levers had bulbous ends. So precautions are good, but weird, unexpected things happen. There's no way to make bikes totally safe, and I think it's reasonably safe to use stem shifters.