Some games you don't need an air force as much to win. In older HOIs I use to forgo a strong air force or create a small elite one. Though I was never deep into HOI3! While in HOI2 and subsequent patches I found that the air power was more so deadly in naval actions. While on land it would cost you ... airfields can be easily over run.
Big Powers can afford air fleets while little powers would probably be better served with a stronger army. I don't really know the full effects of air power in game. It has been presented but it doesn't appear so far as I can tell deadly unless I slept through all the twitchchannel. I don't recall watching Naval Strikes on ships as in WW2 knocking entire fleets. As they did very very effectively.
We won't know exactly what the value in air power is in game till we ourselves test the game then according tweaks will need to be made. 1 German Pilot Rudel killed (what would Allied Pilots of accomplished had they started earlier?)
519 Tanks
800 vehicles of all types
150 Mixed arty
4 Armored Trains
not including supply and naval destruction... on the Eastern Front
Now I will trade that for 1 tank but in game do you get that type of effect? I don't think so? Maybe for balance but I would use a group of 4 Fighter Bombers on land in Hoi2 DH to clean out a slow moving Division in Africa. When they become extremely experienced it was doable as slow as they march. Real? I think so given the situation.
Given that military factories are used both to build the equipment your army need as well as building the aircrafts your airforce need, your airforce and army is in direct competition with eachother in terms of resources as each factory that build aircrafts could be used to build army equipment and vice versa.
A strong airforce can halt the enemy army, making it easy to encircle and thus minimize your own casulties. Air force can also be used in a more direct offensive role and destroy enemy factories. Not only that but it can also play a key role at naval engagements.
However without a strong army your country is likely to face defeat and be annexed, but an army without an airforce will likely not do well and take huge casulties. You will also have alot of trouble to defend your factories, even the strongest army can not defend its factories from enemy aircrafts. An army can not really do to much against a navy which can be a huge deal.
It will cost alot to build up an airforce as aircrafts are extreamly expensive in HOI4, a fighter cost about as much as a heavy tank.