Children’s Sunday School? The Importance of Reaching Local Lost Kids

Often in the family integrated movement, it is taught to have no form of children's Sunday school. Should the whole family be together the entire time? Is it unbiblical to have a children's Sunday school? What about the topic of "ragged schools" and outreaches to lost children? As a church, are you willing to reach out to the lost kids in rundown neighborhoods and even bring them into the church, where it might be "clean," risking your kids getting lice from them in order to share the Gospel with them?