Actually I would argue that the U.S. Army has traditionally not been made up of citizen-soldiers, but instead of professionals. Post Civil War and pre-WWI the Army was a small professional body augmented by volunteers as needed. Post Vietnam, the Army is exclusively professional. The closest thing to the ideal of the "citizen soldier" are National Guardsmen and reservists, but they do not in any way formulate policy or direct anything.
But the U.S. Army is not responsible for internal security. The National Guardsmen do that.

Having said that, Americans understand that their military are not a separate class in a way the class obsessed British don't. The G.I Bill encourages US military personnel to attend college and interact with ordinary Americans. Many US soldiers are short service, they get back to civvy street after a few years.