Excellent question. It does take the issue to the philosophical/conceptual level. So here goes...
When the aircraft was invented, the idea of weaponizing the new invention was not dismissed. In fact, the idea of a 'combat aircraft' was quite immediate once the heavier than air flying contraption was proven to be inevitable.
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Dirigibles and gliders do not have the level of situational (re: tactical) controls, speed, and flexibility like a fully manned and powered aircraft would.
Now for the army...Any army...Not just the US Army...
The army have a limited view of combat. Am not saying that as an insult or even as an insinuation about the army's intelligence. What I mean is that for ground forces, the enemy is always immediately in front, meaning within visual range. Sure, the enemy maybe behind the hills or just a few day's march behind the mountains, but essentially, the enemy is always in view or very soon to be in view. Further, the enemy will be fully formed, meaning the combatants, whether they are human soldiers or tanks or trucks, are fully weaponized and readied to fight.
So if air power is available and under army control, air power will be equally limited in scope in terms of philosophy of combat and war doctrines. The aircraft's deployment will be limited to the front lines. It is not that the army's leadership are ignorant of factories that builds tanks or oil refineries that provides fuel that support the enemy. It is just that for all of man's military history, war have always been 2 dimensional (flat) and at best a few days in the future in terms of planning.
Air power proponents realized the philosophical/conceptual limits that ground forces placed upon the aircraft and fought for institutional severance, not merely organizational autonomy.
The US Air Force is an institution.
The US Army Air Corps is an organization. Even though throughout WW II the airmen were free to plan and fight as they see fit, the 'Army' in USAAC clearly commanded the viewer to note who is the final authority of US air power: The US Army.
If warfare is to be expanded into the third dimension, air power must be allowed to be institutionally free to develop its own war doctrines. The capability is already apparent. It is to attack the enemy behind the front lines and in ways that would both distract and deprive him of his resources. The question is how far behind the lines and how far into the future.
It takes about one week to turn crude oil into quality gasoline, then a few more days or even weeks to supply the enemy's ground forces. So if the refinery is destroyed, we are looking at affecting the course of the war in terms of months or even yrs into the future. Not only that, if the enemy country is defeated, the course of relations to that country will be affected for decades. Air power must be institutionally independent to develop its own methodologies, technology, and war doctrines to achieve goals that far into the future. Philosophically speaking, air power ranks up there with the horse and the wheel, far above the bow and arrow or the machine gun or artillery, in terms of affecting how wars and battles are planned and engaged.
Naval aviation is organizational, not institutional, and subordinate to sea power goals, the same ways the USAAC was subordinate to the US Army. Naval aviation depends on the navy while the air forces are independent. This does not mean naval aviation is any less important regarding contribution to the war effort. It only mean that the exploitation of air power must be appropriate to the character of the service and its goals.
Hope that helped.