I find this mysticism around the US military to be puzzling. I mean really, "The honour of the professional soldier in a modern western democracy is that they don't pick and choose the wars they fight in"? As opposed to every other soldier ever? And when it's a volunteer military and you sign up after a war is declared, that's choosing to fight that war.
I'm not American, so I have no idea about whatever "mysticism" you are talking about.
All soldiers should be honoured for the fact that they volunteer for very dangerous activities, usually will little understanding of when and where those activities will be.
Your point regarding post-war sign ups is valid, but like I said, if you want to fight wars you can just join blackwater et al. If you want to serve your country you can join the nation's armed forces. There is an element in public service in the soldier that should be commended.