Also, with history as our guide, Colin Powell prosecuted the invasion of Iraq from an “advisory” position; Ch-JSoC.
Schwarzkopf from CentCom ran that war. Franks from CentCom ran the 2nd. JCS are advisors, not combatant commanders. There are 6 Combatant Commands; PaCom, NorthCom, EuCom, AfriCom SouthCom, CentCom. They do the planning and execution of operations in their assigned areas.