Not to defend or excoriate any past or future FAA administrator, but nowhere in that job description does it say anything about the officeholder flying anything. It’s a management job and it matters not one iota what hardware (if any) is involved. The Administrator is called a “bureaucrat” because s/he runs a “bureau” which could be responsible for literally any aspect of federal government. Experience at the helm of just about any huge, lumbering, budget-constrained governmental organization is all that is really necessary. That’s an entirely different skillset from flying that a million hours of CRM experience won’t provide. The best candidate needs to be a skilled politician (his actual workplace) who’s smart enough to hire and utilize staff who know aviation and how to manage its constituent parts.