The SG is not "the nation's top doctor", s/he is not even close to being the top doctor in the building where s/he works. The Assistant Secretary of Health position, which is usually filled by a physician, dwarfs the power of the SG in every respect.
When I point this out to public health advocates, they usually become indignant and huff "But Dr. Koop...". Dr. Koop was and is flat out a remarkable person (and a newlywed at 93!) but he would have been a great public health leader whether he took the SG job or not.
Photo of Koop is a U.S. Government Work