If I had a child, and he or she wanted to play, then yes I would be all for it. Unless you live in a town that is insane for football like on that Friday Night Tykes show, then honestly I don't think your child runs the risk of any serious injury.
I played football up until high school, and the worst injury I ever suffered was from some * that liked to pull on your face mask and cut my face.
I think with the right type of coaches and integrity, a lot of injuries can be avoided. I would have zero complaints about my kid playing.