Should I have an Airforce general?

From my experience, I really did not need an air force general to complete campaign, although they come handy when you need to perfect some missions. Here is my take on it:
If you are in early stages of the game, you absolutely don't need one, BUT If you insist on getting one, you probably should get paratrooping general (Student, Kesselring) because they serve as your (secondary) infantry general. When you enter pacific, you get Arnold as your free general for allies, so you don't really need an allied air general.
If you are in later stages of the game, and you have your infantry generals sorted out (both Yama and Runstedt or Kuribayashi instead one of them), for axis, I don't think there is a reason for paratrooping general, but instead get Yamamoto who is THE best AIR general in the game. He deals 10 more damage than Kesselring in cities, Which is significant. For allies, although you don't really need one, get Dowding, who is slightly better than Halsey, just because he deals more damage in cities, and air aura isn't as useful as other auras.
So basically I don't see why would someone get an air general early game, and in late game get Yamamoto