In a lot of systems you swear to a party, a dynasty, or a leader who does not leave. Here the oath is to a document the people can amend and the officers must obey.
Watch a naturalization court on a Friday morning. People who were not born here recite words about supporting and defending the Constitution. They are not becoming subjects. They are becoming the sovereign.
Marines take a version of the same bet: defend the Constitution against all enemies, foreign and domestic. The uniform is not the point. The limit on power is. Michael Gist took that oath. He later stood in a public-school classroom and tried to hand the same idea to kids who had not yet voted — that they own the country, and the country does not own them.