Actually, it is a pretty good descriptive.
I had the pleasure of having a previous HHS secretary on my Board. When I asked him how he enjoyed being the HHS secretary vs governor (he had been the head of our state's legislature and later went on to governor of my state before accepting a position as HHS secretary), he said hated being HHS Secretary and eventually, the staff at HHS wore him down and he left.
When I asked why, he said the career bureaucrats realize that political appointments are transitory and that they can resist by slow walking any reforms these appointed secretaries try to implement. They are also almost immune to firing, because long before the process is complete, the appointees move on.
This hints to what the "deep state" is. It is the power of bureaucrats to effectively ignore those elected by the people and to impose their own ideas through regulations and other powers given to their agencies by virtue of their positions without fear of losing their jobs. Perhaps to break the power of the deep state, we need term limits on many senior positions in those agencies along with stricter oversight and the ability to terminate them on short notice (again for senior positions only, not the rank and file).