I saw a lot of this in county government combined with cronysism. Luckily most of the top people do not do a lot of work.

The Peter Principle is the principle that “in a hierarchy every employee tends to rise to his level of incompetence.” It was formulated by Dr. Laurence J. Peter and Raymond Hull in their 1969 book The Peter Principle, a humorous treatise which also introduced the “salutary science of Hierarchiology”, “inadvertently founded” by Peter. It holds that in a hierarchy, members are promoted so long as they work competently. Sooner or later they are promoted to a position at which they are no longer competent (their “level of incompetence”), and there they remain, being unable to earn further promotions. This principle can be modeled and has theoretical validity.[1] Peter’s Corollary states that “in time, every post tends to be occupied by an employee who is incompetent to carry out his duties” and adds that “work is accomplished by those employees who have not yet reached their level of incompetence”.