Thought Experiment: How has Airpower worked in Real Life?
(Because I've been reading a fair amount about the air war over the Soviet Union lately, preparing a new chapter or two for the new book)
Air Force technique and doctrine have always been based on one of two basic functions: Strategic and Tactical.
Strategic is the attack on enemy Nation: bombing factories and sources of military equipment, railroads and other transportation systems, terror bombing of cities to directly kill or discourage the entire enemy population. It has the advantage (for the air force) of being almost completely independent of what anybody else is doing, so the Air Force can pursue it without reference to the rest of the military. Also, because the effects are rarely apparent right away, they can claim tremendous results without any proof at all. The fact is that Strategic Bombing has only been effective if enormous resources were used for it and it went on for a long time: years, in fact. Strategic Bombing Light, as done by the German Luftwaffe, Japanese, Italian or Soviet air forces in WWII, never had a strategic effect: the best the Luftwaffe did was to terrorize a single city for a short time, as at Rotterdam, Belgrade or Warsaw, and only as part of a larger land campaign. The attempt to use strategic bombing against Moscow in 1941, for instance, was almost completely ineffective and only served to keep German bombers from doing anything really useful while they concentrated on Moscow without results.
Tactical Air Forces are designed to directly effect the ground or sea war. Consequently, and in contrast to Strategic Forces, they are generally used within a short range of the front line or fleet, designed to rebase to keep up with the movement of the rest of the forces, and concentrate on ground support missions like Reconnaissance, Front Line Attack, or attacks on enemy artillery, HQ, and supply lines directly behind the front ("directly behind" depends on the technology: it was no more than 50 - 200 kilometers for the first half of the 20th century, today it is more like 100 - 500 kilometers with modern Strike Aircraft)
So, I suggest that 'Air Force' comes in two distinctive types: a separate mechanic to attack enemy cities, Industrial and other Districts, Improvements, and an adjunct to the army and navy that extends the range at which they can attack enemy Units opposing them.
The latter could even be represented as Points added to combat factors or applied in an Extended range (3 - 5 tiles) as Vision (Reconnaissance or Artillery Spotting) or Tactical Bombing (combat factors). The explicit advantage of Air Power is that those Points could be held to be applied to support any Unit within a radius - tactical air forces can rebase and start attacking in an entirely new area within hours, days, or weeks at the most, and this mobility and flexibility is one of the great strengths of this type of air power.
Strategic Air Power requires a Huge investment in heavy aircraft, bases for them, repair and training facilities, and development of certain techniques that don't apply anywhere else: like the capability of putting 1000 large aircraft in the air in the same area and direction from numerous bases and concentrate them all over a target precisely in time and space 100s of kilometers away. Strategic Air Power that actually works is extremely expensive: so much that in the largest war in history, when every participant was straining every resource to the max, only two Civs built real strategic bomber forces: Britain and the USA. The Heavy Bomber organized, trained and supported as a Strategic Weapon should be pretty rare in the game. To this day, baring the use of nuclear weapons, only the USA really has a strategic bomber force large enough to have much effect, and note that Russia's strategic force with non-nuclear missiles and bombs in a year has utterly failed to break Ukraine or even constrict its military production much. The massive destruction of Ukrainian cities has not been due to any strategic bombing by either aircraft or missiles, but from ground bombardment by army missiles and artillery. In WWII terms, it is Stalingrad writ large, not Dresden or Hamburg.
Just thoughts, but it should be noted that the flexibility and variety of Air Power tactical applications is not necessarily represented well by separate Units on the map, given that IRL those 'units' could be applied to several places and actions within a single turn.