In most western nations the top civil servant and all those below them are non-partisan career civil servants that keep the ship running at all times and have better employment protections than the average employee (which already requires for cause in those countries).
A new Minister’s (Secretary in US parlance) role is mainly that of someone who plots a course and the civil servants in the ministry try to follow it.
As a side note, the concept or “government shutdown” is also entirely foreign in those countries, if not outright ridiculous.
For example, they might create an Administration of Land Management with authority over all extraction rights on federal land, funded by fees paid for those rights, and with a director the President cannot remove except for cause.
And it wouldn't be possible for Democrats to change that until they too won the House, Senate, and Presidency at the same time.
A government full of agencies like that would make elections mostly irrelevant, and things would change only when one party won everything.
Many also have a House of Lords or Bundesrat or something similar that is not elected by the people, whose purpose is to make the government less democratic. We should not try to be more like those governments.
Of those that remain, how many have agencies not subject to the chief executive like the CFPB?