<<As radical as this sounds, I think the person holding supreme power over the military should have some military experience.>>
The Constitution says otherwise, and the electorate seems to follow the Constitution. Nothing prevents a civilian President from appointing military aides who can guide him through the technicalities. If the Prez is halfway bright, he should be able, with some good, solid advice, to size up the situation and manage it appropriately. FDR didn't do too bad a job of managing his war, despite his lack of military experience, while JFK, LBJ and Nixon, all with some military experience, collectively did a standup job of starting, totally fucking up and then losing the Viet Nam War.