Why would you treat children with coarctation of the aorta?

Why or how? The how is already answered by dr. Rubin. If your question is why treat coarctation it is to improve blood flow to the organs of the lower part of the body, prevent severe high blood pressure in upper part of body causing headache, dizziness, nosebleeds, shortness of breath and to prevent eventual development of enlarged heart and heart failure.
Heart Failure. Mostly we may treat coarctation because it often puts a severe strain on the heart muscle, which can lead to permanent heart damage and even death. The cure is generally surgery.
Blood Flow. If a child is diagnosed with coarctation, then the circulation of blood is almost certainly negatively effected. Infants that present with coarctation require life-saving treatment to get blood to their body. Older children require surgery to re-establish normal blood flow. Without treatment, they will develop hypertension as well as have extra work loading on the heart. These are not good.