Children need lots of protein to grow, but this doesn't mean they necessarily need a supplement. Remember that the 7 grams in an egg, for instance, represents a far higher percentage of body weight for a 35-pound body than for a 150-pound body.
However, as long as a child has a healthy, balanced overall diet, there is no risk in giving them a moderate amount of a high-quality powder. For instance, if you are already making shakes or protein-rich baked goods for yourself, it's safe to share them with your children.
Unfortunately, most of the foods kids snack on are usually high in sugar and simple carbohydrates, which is one reason childhood obesity is such a problem. By creating more balance in their diet and tilting the scales slightly toward a higher protein intake, you'll not only help fuel their physical activities, but also promote a leaner body composition in their formative years.