Its not like every time there's a new president every single person in the government is fired and new people are rehired. Its also not like every policy/law gets shredded and entirely new policies get created overnight.

Having a new president is like a new captain giving orders on an incredibly massive ship. There's a ton of inertia going on, there's a lot of people below the captain that are still the people with the hands on the controls operating the boat. Plus, usually when you're in the middle of trying to steer the boat to port the captain gets replaced and starts commanding the boat turn to starboard.

Coupled this with the idea that its not really just a single ship, its a fleet of 50+ ships each with that same concept of a ton of inertia at play and not really a strict chain of command between the captains of each ship and the admiral of the fleet (imperium in imperio).