While I think the stated concern about a 'deep state' is rather exaggerated, I think there is a legitimate concern about friction between the executive and the bureaucracy. There is broad tradition of non-partisan civil service taking orders from the partisan government of the day across the Western world, and it exists for two very good reasons: If the civil service is partisan, worthy public servants will lose their positions upon any change in government; and if the civil service is partisan, governments will not trust them.

We saw this in Canada under the Harper government in the early part of this decade, with civil servants actively undermining the government and the government retaliating with gag orders; it didn't take long before the government, knowing that any research they asked for would be leaked in the most damaging way possible, abandoned evidence-based governing in favour of seat-of-the-pants policy-making.

Now, what took a decade in Canada seems to have happened in a matter of weeks in Washington; but the fact remains that when the civil service is overtly opposed to their political masters, good government becomes impossible. It's one thing to have a bungling fool in charge of the ship of state; it's quite another to have a bungling fool who knows his crew are in the process of staging a mutiny.