EDIT: This thread was meant to be about Strategic Bombing, not Air Superiority(despite them being closely linked).
Speaking within the years of WW2 - Present, has air superiority ever actually have the highly talked about effectiveness top US Chiefs state it has?
In World War 2, did we really "cripple" the German and Japanese ability to wage war? Or was it a complete exaggeration and abuse of power(i.e firebombing in Japanese Cities). It's almost as if the air campaign never existed, the same outcome would have come to... The dropping of the Nuclear Bombs.
Moreover, it's tertiary purpose constantly stated is that is 'breaks the will' of the people(and their support) but history seems to show that all it does is the exact opposite. It unites the people.
This is especially true in Vietnam. The magnitude of bombs dropped was unfathomable, and the complete opposite effects the bombing campaign had, across the board, was nothing short of astonishing. It not only didn't accomplish what it set out to do, it hindered the war effort in literally every possible category(Lack of Peace Talks, Civilian Hatred, etc.).
Of course, Vietnam was a complicated matter, and one can argue that in hindsight, air superiority or anything for that matter, wouldn't* have changed the outcome.
Aside from being instrumental in destroying the enemy casualty wise, It's just not as effective as the books make it seem to be.
Short answer:
You're confusing two quite distinct issues here: "air superiority" and "strategic bombing". This subject has been studied at great length.
Discussion:
"Air Superiority" is the capacity to do what you please in the air -- that could be strategic bombing, it could be tactical air, it could be transport, could be reconnaissance. You have "air superiority" when the enemy can no longer threaten vulnerable air assets (like transports and bombers) with their own fighter aircraft.
"Strategic bombing" is just one component of what you do when you have air superiority (indeed you can do it when you don't, but you incur higher losses -- the Germans in the Battle of Britain, for example). By the latter days of the WW II, the US had "complete air superiority" over Japan-- essentially could fly bombers without escorts.
The effectiveness of strategic bombing has been the subject of study, for many decades. The most famous of these studies was "The United States Strategic Bombing Survey", comprising some 208 volumes for the European theatre and 108 volumes for the Pacific.
So yes, If you start reading now, you might finish in a decade or so . . .
. . .but first and most importantly, you should understand that "air superiority" and "strategic bombing" are not at all the same things. Strategic bombing as fundamentally economic in conception -- destroy the enemy's ability to carry out war; its relatively disconnected from the battlefield at the time.
Air superiority, on the other hand, is very much connected to the present battlefield. The D-Day invasion is a good example; air superiority was required to provide the capability for all sorts of vulnerable transports-- landing craft, gliders, and so on.
There has been a great deal of study of just what effect US bombing had on both Japan and Germany; the short form is "less that strategic bombing advocates imagined and had hoped for, but still substantial". It remains controversial as to whether more air resources should have gone to tactical air vs strategic bombing -- eg would you have gotten more net war winning military effect out of 3 P-47s than one B-17 (assuming that the resources required to build and operate one four engine B-17 are roughly equivalent to those required to build and operate three one engine fighter bombers).
There is even a substantial academic industry in analysing just how the Strategic Bombing Survey got written, and how institutional biases might have contributed to its conclusions. There have been subsequent studies of air operations in Korea, Vietnam and the Middle East-- but for the most part these weren't "strategic bombing campaigns", because degrading industrial capacity was a far less important objective than it was in the Second World War.
Sources: