management experience in a significant part of those responsibilities...from the link...
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The FAA carries a huge responsibility – from directing air traffic in and around the nation and helping ensure protection of the public during space launches, to airport safety and inspections, and standards for AIRPORT DESIGN, CONSTRUCTION, AND OPERATION; regulating flight inspection standards and advancing satellite and navigation technology, to developing and maintaining the Next Generation Air Transportation System (NextGen).
To accomplish all this and more, the FAA RELIES ON THE TALENTS OF A DIVERSE GROUP of aviation, technical and business professionals to perform a variety of hands-on functions that keep air travel moving freely and safely. (emphasis mine)
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Bottom line...Mr. Washington was CEO of Denver Int'l Airport (3rd busiest in the U.S.), and CEO of L.A. Metro, handling all the business, construction, personnel and bureaucratic issues involved in a major city's transportation needs....btw, how many pilots have that level of experience which is needed to Administer the FAA?
Link: https://www.faa.gov/jobs/who_we_are