Who should run NASA: a scientist or a bureaucrat? I don't have the answer, but I will share a little vignette from history (because I'm an historian) that I think is interesting and relevant... Please read on!
The Administrator typically changes with each President, usually to be politically in-line with the administration. When Kennedy took office, he wanted Jim Webb for the job.
Jim Webb arrived in Lyndon Johnson’s office on Jan. 30, 1961. The lawyer turned lobbyist and businessman who had been head of the Bureau of the Budget and as under-secretary of state during the Truman administration was wary of taking the job. NASA was considered a boondoggle.
Space stations and lunar missions were on the books for 1970 or later, so in the meantime, whoever ran the agency would have to stand up to the military trying to wrest control of space activities while managing an agency that might kill an astronaut in front of the whole world.
Not to mention, belief in Washington was that the country would lose interest soon enough. When the glamour of space faded, it would take its administrator down with it. It was, in essence, a career killer.