The government is not just the president and the buddies he brings in. There are many departments that need to operate after the president and his crew leave office. All of those have a vested interest in keeping their jobs and being able to operate after the next election.
It's no deep state conspiracy that the Pentagon or the CIA have their own opinion on world politics. If anything, the Trump administration has shown that there are still some restraints to the president's power. At some point details were made foggy or even left out in Trump's security briefings out of fear they might get leaked to Twitter. The end result of this process isn't to keep the elites in power or to control the people, it's much more tame than that. People don't like change and when a new guy rolls in and decides that the way some government body does something is wrong, people will naturally resist.
There is always a power balance, usually in favour of the democratically elected officials, between the elected government and the government that sticks around. When push comes to shove the elected officials always have the power to overrule the unelected ones, but any future endeavours related to these parties would become difficult once you force matters.
The CIA, FBI, DoJ and FDA don't get a complete reshuffle every four years. The figureheads and even organisational top can get replaced, but there are many layers of middle management below them that have cemented their ways in difficult to change processes, workflows and office culture.
The system has its advantages, notably that the country doesn't collapse after giving a complete lunatic the reigns for four years, but also a great many disadvantages, notably elected officials being worked against in their quest for improvement and change. This effect can be increased or decreased, but it won't ever go away and denying that there is more to politics than elites at the top is just nonsensical in my opinion.