This freedom of the skies thing is a bit over-rated. I read recently that when the Germans had been kicked out of Normandy in 1944 after being harrassed by our wonderful RAF fighter bombers,when post conflict teams went and examined the battle debris they found that the effect of air power was less than the RAF had been claiming.
After the last world war France lost wars in Indochina and Algeria where they had total freedom of the air. Even more spectacularly the Americans with a crushing air superiority lost to a peasant army in Vietnam, and today are losing to Afghan peasants. The Soviets also lost in Afghanistan with total control of the air (apart from the later stages when their helicopters were being shot down with US supplied Stinger Missiles).
With regard to the Battle of Britain when you explode the myth of the few and the Blitz, you also chip away at the reputation of the great myth maker, the man resonsible for the Norwegian balls up, in its time as half baked as Gallipoli in 1915.
Interestingly, in Indo China, in Dien Bien Phu, the French start off with total command of the air, but then have to confront the Viet anti-aircraft fire, and then the direct artillery fire onto their airstrips and landing zones. Little men in pyjamas clearly have not read the air warfare doctrines and have not yet learnt how to lose their battles.
As to 1944, there was, of course, that little operation called "Market Garden" - perhaps the greatest exercise of tactical air power (numerically, at least) in the history of mankind. And, er ... we lost. And you are right about Falaise - the damage done by "air" was vastly overstated, and the bulk of the damage was done by machine-gun fire rather than rockets and bombs.