Not sure why by implication this thread questions the need for an independent air force. Thought when the Americans decided after Korea to follow our example everyone had learned the lesson from the experience of war.
Air power is necessarily a limited resource because it is expensive. If you have a limited resource and conflicting priorities the management and allocation of that resource had better be independent of the other forces clamouring for support – otherwise he who shouts loudest/wears the highest rank/has the biggest willy wins.
Air power is also complex and requires highly skilled technicians and aviators. If the air elements are competing for spending with the tank or the ship it is unlikely that they will get their appropriate share.
The management of air power is also highly specialised and to do the job successfully requires more than a career shared between maritime and soldiering.
Just a few thoughts.