Politicians have people skills and lawyers know how the system works, both attributes which are actually needed to run a government well.

As an example, consider Laplace, one of the cleverest mathematicians in history, who got fired from his ministry position after six weeks.

Geometrician of the first rank, Laplace was not long in showing himself a worse than average administrator; since his first actions in office we recognized our mistake. Laplace did not consider any question from the right angle: he sought subtleties everywhere, only conceived problems, and finally carried the spirit of "infinitesimals" into the administration.