SASless..I think I get your last point..but a small technical point.
You state that an Air Force might be required as an Air Corps might not be sufficient.
A Corps (in this sense - as opposed to a formation between a division and an Army) by definition is a structured military organisation / body of men (et al women ..PC) with specific specialisation - flying.
Ergo it can be as large a structure as you require it. So by definition an entire Air Corps could achieve dominance, superiority or supremacy.
Was not the US Army Air "Corps" made up of smaller Air "Forces"? Until there was a need to diferentiate the new USAF (circa 1950's) from its Army origins - the name was cosmetically changed.
The UK had a Army Royal Flying Corps 1912, in favour of an Army Air Corps (circa 1910). The Royal Air "Force" was adopted in 1918, again to distance itself from its birth in the Army. The current UK Army Air Corps (circa 1957 - there was an itteration between 1941 - 1950) is much, much smaller than the original USAAC and operates akin to US Army Aviation.
