Should a personal statement for grad school discuss large challenges in personal life?
My own experience includes the opposite of what you describe. I have evaluated statements of purpose (SoP) with specific stories of overcoming adversity where the story helped me conclude that this was a courageous person worth taking a shot at. This was, of course, accompanied by strong grades (though not necessarily stellar) and supportive letters.

I strongly disagree with your notion that an SoP can only hurt you.