Italians...
Yes, the whole concept of air-power was heavily linked with the facists in the 1930's.
The Italians staged the Trans-atlantic crossing with a number of sea planes to show that numbers of planes could traverse great distances.
The British were fixated on the idea of Strategic bombing, and of the time considered that in any war France would surrender if Britain could bomb paris as the French were considered to be inferior in morale to the British. In the US, the Japanese were never considered a threat as it was believed that Japanese would make bad pilots as they had a bad sense of balance.
(It wasn't just the nazis to have radically strange racial ideas!).
My first degree was in War Studies at King's College London, and there was a very interesting series of lectures on the growth of air power. Amusingly our profesor concluded that air-power is essentially a fasicst idea, which did not go down well with the RAF and USAF students in attendance!
As already mentioned, the Italians had the leading airforce in the 1930s, but by 1940 much of it was obsolete. The Nazis had a similar problem, Hitler only reckoned on a brief war and didn't have extensive planes to upgrade Panzers, and fighters etc - as a result the Germans got caught in a similar trap during the early 1940's - it is argued that designs like the Panther could have been in production earlier, and had Hitler just allowed one design, rather than have a wide range, but few actual models of 'wunder' tanks, Germany could have concentrated on building large numbers of one type of tank.
In any case, as nice as the Air Sprites are - air combat in HOI still leaves much to be desired. Whilst the EU engine is very good for creating the ground battles, and to a lesser extend the Naval battles, the air aspect is very disapointing.
I feel Strategic Bombing should be abstracted more to represent a general bombing campaign of different targets, going for the factories - forcing AA production, and redelpyment of fighters - but at the moment transport planes intercept bombers, and even nuclear tipped ICBMs - which is crazy. I'm not so sure the tactical bombing and dive bombing is implemented well - I would rather attach air units to certain divisions which greatly increases their combat ratings.
Certainly in the case of the Germans, the Luftwaffe initially was subordinated to the Army, as a tactical air-force which gave a major advantage. Later in the war, the allies enjoyed increased attack and defense capability due to the tactical airforces developed.
Games such as 'Advanced Third Reich' and other Avalon Hill games tend to simply boost combat ratings to represent air power. I think this would make more sense... (this probably belongs in another thread).