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.
or: Why Everything Is Terrible, An Overview.1
It sounds like a theory which explains too much. But it's not a theory, hardly even an explanation, more a pattern that manifests itself once you start trying to seriously answer rhetorical questions about the state of the world. From many perspectives, it's obvious to the point of being mundane, practically tautological, but sometimes such obvious facts are worth pointing out regardless.
The idea is this: The subset of participants which rises to prominence in any area does so because its members have traits helpful to becoming prominent, not necessarily because they have traits which are desirable. Thus, without ongoing and concerted effort, a great many arenas end up dominated by players employing strategies which are bad for everyone.
This comes up again and again: