That reason is alerting people around you to things going on. If I see a firetruck going past my office, I'm going to want to know where it's headed, for a number of reasons (is there anyone I know involved, are people safe, am I going to be delayed getting home, am I in any danger). Local news isn't going to pick up every fire department response.
Or in more positive ideas, a spontaneous block party is happening down at the local ice cream shop. I'd love to walk down there, but I don't know it's happening. Hyper local services would be incredibly useful with leveraging technology to bring a community closer together. Twitter could solve this problem, but I need to know who to follow. With hyper-local services like Yik Yak, I wouldn't need to follow anyone. The information would just be there.
>if taking down an app could save a kid's life then shouldn't we do it?
It's not technology's problem, it's society's. We could save millions of lives by getting rid of cars. Thousands by getting rid of cell phones. There's a reason we don't do that. There's a much easier answer to the problem of how to protect children from being bullied on Yik Yak: teach your kids the value of walking away.