It was essential for the air war. The air war beat Japan, even though the air war didn't beat Germany.
It is true the air war didn't beat Germany but both strategic and tac air played a very large role.
I think the war in Europe would have looked very much different post D-Day without the cumulative drubbing the Germans took from the air before and after the landing.
While the outcome would probably have been the same, I believe the cost would have been very much higher.
The Germans lost tremendous amounts of material and heavy equipment not to mention men whenever they moved. Logistics was simply a nightmare.
Monty might still be trying to take Caen without the 2000 bombers that supported the British operation Goodwood.
