Whenever we tried giving command and control of the air component to one of the other components during war games, it did not end well because none of the others seemed to understand that the air was a battlespace in its own right and has to be fought as such, just as the others are. There are 5 components, land, maritime, air, space and cyber. While at any one time, any of these can be the supported component, my experience is that it is best if they are fought in their own right to support the commander's plan.